บทที่ 3 การวิเคราะห์และนำเสนอข้อมูลเชิงปริมาณ 1-2565

บทที่ 3 : การวเิ คราะห์และนาเสนอข้อมลู เชิงปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 150

8. สายการบนิ แหง่ หน่ึง ได้สารวจความพึงพอใจของผู้โดยสาร ต่อการใหบ้ รกิ ารของพนักงานต้อนรบั บนเครื่องบนิ ซึ่งมี
คะแนนเต็ม 10 คะแนน โดยสารวจจากผ้โู ดยสารที่สุม่ มาจานวน 20 คนไดผ้ ลสารวจโดยเรียงคะแนนจากนอ้ ยไปมาก
ดงั น้ี

135578 888 8
8 9 9 9 9 10 10 10 10 10

8.1) จงหาควอรไ์ ทล์ที่ 1 ควอรไ์ ทลท์ ่ี 2 และควอร์ไทลท์ ่ี 3 ของขอ้ มูลชุดนี้
8.2) ข้อมลู ชดุ น้ีมีค่านอกเกณฑห์ รือไม่ถา้ มคี ือค่าใด
8.3) จงเขียนแผนภาพกล่องเพื่อนาเสนอขอ้ มลู ชุดนพ้ี รอ้ มท้ังอธิบายลกั ษณะการกระจายของข้อมลู ชุดน้ี

วธิ ีทา 8.1) หาควอร์ไทล์ท่ี 1 ควอร์ไทล์ท่ี 2 และควอร์ไทล์ที่ 3 ของข้อมลู ชดุ นี้
โดยเรียงคา่ ของข้อมลู ตามตาแหน่งท่ขี องขอ้ มูลจากนอ้ ยไปหามาก

ตาแหนง่ ท่ี 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

คะแนน ( )

( ) ( )8.1.1) ค่าต่าสดุ
ของขอ้ มลู คือ ............................................ ค่าสูงสดุ ของข้อมูล คือ ................................................

และ จานวนขอ้ มลู ข้อมลู = ............................................

8.1.2) หา 1 , 2 และ 3 หาไดจ้ ากสูตร ตาแหน่งควอไทลท์ ่ี = ( +1) เมอื่ จานวนขอ้ มูล = ……………. ดงั นี้

4

อยู่ในตาแหน่งท่ี8.1.2.1) 1 ...............................................................................................................................................................................................................................................

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ดังนน้ั คา่ ของ 1 ....................................................................................................................................................................................................................................................................................................

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บทท่ี 3 : การวิเคราะหแ์ ละนาเสนอข้อมูลเชงิ ปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 151

อยู่ในตาแหน่งที่8.1.2.2) 2 ................................................................................................................................................................................................................................................

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ดงั นนั้ ค่าของ 2 ...........................................................................................................................................................................................................................................................................................................

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อยูใ่ นตาแหน่งท่ี8.1.2.3) 3 .............................................................................................................................................................................................................................................

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ดังนั้นค่าของ 3 .............................................................................................................................................................................................................................................................................................................

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8.2) ข้อมูลชดุ น้ีมีคา่ นอกเกณฑ์หรอื ไมถ่ ้ามคี อื คา่ ใด : หาค่านอกเกณฑ์

หาค่า8.2.1) 1 − 1.5( 3 − 1) = .....................................................................................................................................................................

= .....................................................................................................................................................................

หาค่า8.2.2) 3 + 1.5( 3 − 1) = .....................................................................................................................................................................

= .....................................................................................................................................................................

จะพบว่า มีขอ้ มูลทีน่ ้อยกวา่ ได้แก่ 1 − 1.5( 3 − 1) .............................................................................................................................................................................

และ มขี ้อมลู ทม่ี ากกว่า ไดแ้ ก่ 3 + 1.5( 3 − 1) ...........................................................................................................................................................................

ดังนนั้ ค่านอกเกณฑ์ของข้อมูลชดุ น้ี ไดแ้ ก่ .....................................................................................................................................................................................................................

บทที่ 3 : การวิเคราะหแ์ ละนาเสนอขอ้ มลู เชงิ ปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 152

8.3) เขียนแผนภาพกล่อง (Box plot) เพือ่ นาเสนอขอ้ มลู ชดุ นี้

∎ สรุปข้อมูลทีไ่ ดจ้ ากแผนภาพกลอ่ ง

9. ผลการสอบวิชาภาษาอังกฤษของนักเรียนกลุ่มหนึ่งซ่ึงมีการสอบจานวน 2 คร้ัง แต่ละครั้งมีคะแนนเต็ม 100 คะแนน
แสดงด้วยแผนภาพกลอ่ งไดด้ งั น้ีโดย

แผนภาพกลอ่ ง (1) แสดงคะแนนสอบครงั้ ท่ี 1 และ
แผนภาพกลอ่ ง (2) แสดงคะแนนสอบคร้ังที่ 2
จงพิจารณาว่าเป็นไปได้หรือไม่ท่ีแผนภาพกล่อง (3) แสดงคะแนนเฉลี่ยจากการสอบทั้งสองคร้ังของ
นักเรยี นแตล่ ะคนในกลมุ่ น้ี

(1)

(2)

(3)

10 20 30 40 50 60 70 80 90

ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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บทที่ 3 : การวเิ คราะหแ์ ละนาเสนอขอ้ มูลเชิงปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 153

10. ผลการสารวจค่าใช้จ่ายเฉล่ียต่อเดือน (บาท) ของครัวเรือนในกรุงเทพมหานคร ที่เลือกมาในตัวอย่างแสดงด้วย
ฮสิ โทแกรมไดด้ ังนี้

จานวนครัวเรือน

400

300

200

100

0 20,000 ค่าใช้จ่ายเฉลีย่
0 5,000 10,000 15,000 20,10000,02050,000 30,000 ต่อเดือน (บาท)

30,000

จงพิจารณาวา่ แผนภาพกล่องใดต่อไปนเี้ ปน็ แผนภาพกล่องทไี่ ด้จากฮสิ โทแกรมขา้ งต้น พร้อมทงั้ ให้เหตุผลประกอบ

ก. ข.
28, 000
24, 000 25, 000
20, 000
15, 000
ค. 6, 000
5, 000

ง.

20, 000 18, 000
15, 000 14, 000
10, 000 10, 000
5, 000

0 6, 000

ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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บทท่ี 3 : การวเิ คราะห์และนาเสนอข้อมลู เชิงปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 154

11. ร้านค้าออนไลน์แหง่ หนงึ่ ตอ้ งการศกึ ษาความสัมพนั ธร์ ะหว่างจานวนเงนิ ทล่ี ูกคา้ สั่งซอื้ สินคา้ กบั จานวนเวบ็ เพจที่ลกู ค้าเย่ียมชม
จงึ สุ่มข้อมลู การสั่งซ้อื สินคา้ มา 40 รายการแล้วนาข้อมูลดังกลา่ วมาเขียนแผนภาพการกระจาย ได้ดังน้ี

จานวนเงนิ ท่ีลกู ค้าสงั่ ซอ้ื สนิ คา้ (บาท)

180
160

140
120

100
80

60
40
20

จานวนเว็บเพจท่ีลูกค้า
0 2 4 6 8 10 เยย่ี มชม (หน้า)

จงพจิ ารณาวา่ จานวนเงนิ ทล่ี กู คา้ สงั่ ซื้อสินค้าและจานวนเวบ็ เพจที่ลกู ค้าเยยี่ มชมมีความสัมพนั ธก์ ันหรอื ไมอ่ ยา่ งไร

ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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บทท่ี 3 : การวเิ คราะห์และนาเสนอขอ้ มูลเชิงปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 155

12. นักวิจัยได้เก็บข้อมูลจานวนสายพันธุ์พืชต่อพื้นท่ี 0.04 ตารางเมตร ณ พื้นที่ที่มีความสูงจากระดับน้าทะเล
ปานกลางตา่ ง ๆ กัน ไดผ้ ลสารวจดงั นี้

ตวั อยา่ งที่ ความสงู จากระดับนา้ ทะเลปานกลาง (กโิ ลเมตร) จานวนสายพนั ธ์พุ ืชตอ่ พื้นที่ 0.04 ตารางเมตร

1 0.64 15.0
2 0.64 20.0
3 0.86 16.0
4 0.86 18.5
5 0.89 13.5
6 0.89 16.0
7 1.22 11.0
8 1.22 19.5
9 1.45 11.5
10 1.45 12.0
11 1.72 8.0
12 1.72 8.5

จงเขียนแผนภาพการกระจายของข้อมูลชุดน้ีพร้อมทั้งพิจารณาว่าจานวนสายพันธุ์พืชต่อพ้ืนที่ 0.04 ตารางเมตร
และความสูงจากระดับน้าทะเลปานกลางมคี วามสมั พันธก์ ันหรือไมอ่ ยา่ งไร

ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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บทท่ี 3 : การวิเคราะหแ์ ละนาเสนอขอ้ มูลเชิงปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 156

13. ผลการสารวจสายการบิน 10 แห่ง ไดแ้ ก่ สายการบนิ A , B , C , D , E , F , G , H , I และ J เกยี่ วกับร้อยละของเท่ยี วบิน
ที่ตรงเวลาและจานวนคร้ังของการเกิดเหตุการณ์กระเป๋าเดินทางสูญหาย (ครั้งต่อผู้โดยสาร 1,000 คน) แสดงด้วยแผนภาพการ
กระจาย ไดด้ ังน้ี

ร้อยละของเท่ยี วบนิ ท่ตี รงเวลา

A D
70 G

60 B

F
EH
C

I

J
50

04 5 6 7 8

จานวนครั้งของการเกิดเหตกุ ารณก์ ระเปา๋ เดินทางสญู หาย (ครั้งตอ่ ผู้โดยสาร 1,000 คน)

13.1) สายการบนิ ใดตรงเวลาที่สดุ และสายการบนิ ใดไม่ตรงเวลาท่ีสุด
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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13.2) สายการบินใดท่ีเกิดเหตุการณ์กระเปาเดินทางสูญหายมากที่สุด และสายการบินใดท่ีเกิดเหตุการณ์กระเป๋า
เดนิ ทางสูญหายนอ้ ยท่ีสุด
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13.3) ข้อสรุปที่ว่า “สายการบิน J เกิดเหตุการณ์กระเป๋าเดินทางสูญหายบ่อยกว่าสายการบิน B ประมาณ 2
เทา่ ” เป็นจรงิ หรอื ไมเ่ พราะเหตุใด
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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13.4) ข้อสรุปที่ว่า “สายการบินท่ีเกิดเหตุการณ์กระเป๋าเดินทางสูญหายบ่อยมีแนวโน้มที่จะตรงเวลา” เป็นจริง
หรือไมเ่ พราะเหตใุ ด
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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บทท่ี 3 : การวเิ คราะห์และนาเสนอขอ้ มูลเชงิ ปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 157

14. กาหนดข้อมูลของประชากรในแต่ละชุดตังตอ่ ไปน้ี
ชดุ A : 5 , 5 , 5 , 5 , 5 , 6 , 6 , 6 , 7 , 7 , 8 , 8 , 9 , 9 , 10 , 10 : พบวา่ ชุด A มีจานวน ................................. ขอ้ มลู

ชดุ B : 1 , 1 , 1 , 1 , 2 , 2 , 2 , 3 , 3 , 4 , 30 : พบว่าชุด B มีจานวน ................................. ข้อมลู

จงหา ค่าเฉลย่ี เลขคณติ ( ) มัธยฐาน ( ) และฐานนิยม ( ) ของขอ้ มูลแตล่ ะชุด

วิธีทา 14.1 หาค่าเฉล่ียเลขคณิต มธั ยฐาน และฐานนยิ ม ของข้อมลู ชดุ A ที่มีจานวนขอ้ มลู = ………………………. ขอ้ มลู

ตาแหนง่ ท่ี 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 รวม

ชุด A : ∑1 =61 =

14.1.1) หาค่าเฉลีย่ เลขคณติ ( ) ของข้อมูลชดุ A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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14.1.2) หาคา่ มัธยฐาน (Me) ของขอ้ มลู ชดุ A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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14.1.3) หาฐานนยิ ม (Mo) ของข้อมลู ชดุ A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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14.2 หา คา่ เฉลย่ี เลขคณิต มัธยฐาน และฐานนิยม ของข้อมูลชดุ B ที่มจี านวนขอ้ มลู = ………………………. ข้อมูล

ตาแหน่งที่ 1 2 3 4 5 6 7 8 9 10 11 รวม

ชุด B : ∑1 =61 =

14.2.1) หาค่าเฉลยี่ เลขคณติ ( ) ของขอ้ มลู ชุด B
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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14.2.2) หาคา่ มัธยฐาน (Me) ของขอ้ มลู ชุด B
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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14.2.3) หาฐานนยิ ม (Mo) ของขอ้ มูลชดุ B
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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บทที่ 3 : การวิเคราะห์และนาเสนอขอ้ มูลเชงิ ปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 158

15. กาหนดขอ้ มลู ของตัวอย่างในแตล่ ะชุดดงั ตอ่ ไปนี้

ชุด A : 2 , 3 , 3 , 5 , 5 , 5 , 7 , 7 , 8 , 10 , 14 , 14 , 19 : พบว่าชุด A มจี านวน ................................. ขอ้ มลู

ชุด B : 0.9 , 1.2 , 1.7 , 2.1 , 2.5 , 2.8 , 3.2 , 33 , 3.7 , 4.8 , 5.7 : พบวา่ ชดุ B มีจานวน ................................. ขอ้ มลู

ชดุ C : 59 , 73 , 82 , 87 , 90 : พบวา่ ชดุ C มีจานวน ................................. ขอ้ มลู

จงหา 15.1) คา่ เฉลี่ยเลขคณิต มธั ยฐาน และฐานนยิ มของข้อมูลแต่ละชดุ

วธิ ีทา 15.1.1 หาค่าเฉลย่ี เลขคณิต มัธยฐาน และฐานนยิ ม ของข้อมลู ชดุ A ทม่ี จี านวนข้อมลู = ………………….………………. ขอ้ มลู

ตาแหนง่ ที่ 1 2 3 4 5 6 7 8 9 10 11 12 13 รวม

ชดุ A : ∑1 =31 =

15.1.1.1) หาค่าเฉลีย่ เลขคณติ ( ) ของข้อมูลชุด A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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15.1.1.2) หาค่ามธั ยฐาน (Me) ของข้อมูลชุด A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.1.1.3) หาฐานนยิ ม (Mo) ของข้อมลู ชดุ A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.1.2 หาค่าเฉล่ยี เลขคณิต มัธยฐาน และฐานนิยม ของข้อมูลชดุ B ทม่ี จี านวนขอ้ มูล = ………………………. ขอ้ มลู

ตาแหนง่ ท่ี 1 2 3 4 5 6 7 8 9 10 11 รวม

ชุด B : ∑ 1 =11 =

15.1.2.1) หาค่าเฉลย่ี เลขคณิต ( ) ของขอ้ มูลชุด B
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.1.2.2) หาค่ามัธยฐาน (Me) ของข้อมลู ชดุ B
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.1.2.3) หาฐานนิยม (Mo) ของข้อมลู ชดุ B
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

บทท่ี 3 : การวเิ คราะหแ์ ละนาเสนอขอ้ มูลเชิงปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 159

15.1.3 หาค่าเฉลย่ี เลขคณิต มัธยฐาน และฐานนิยม ของขอ้ มลู ชุด C ทมี่ จี านวนข้อมูล = ………………………. ข้อมลู

ตาแหน่งที่ 1 2 3 4 5 รวม

ชดุ C : ∑ 5 =1 =

15.1.3.1) หาค่าเฉลย่ี เลขคณติ ( ) ของขอ้ มูลชดุ C
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.1.3.2) หาคา่ มัธยฐาน (Me) ของข้อมูลชุด C
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.1.3.3) หาฐานนิยม (Mo) ของข้อมูลชดุ C
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.2) หาพสิ ัย พิสยั ระหว่างควอร์ไทล์ สว่ นเบีย่ งเบนมาตรฐาน และความแปรปรวนของข้อมูล

15.2.1 หาพิสยั พิสัยระหว่างควอร์ไทล์ ส่วนเบยี่ งเบนมาตรฐาน และความแปรปรวน ของขอ้ มูลชุด A ที่มจี านวนขอ้ มูล

= ………………………. ขอ้ มลู

ตาแหนง่ ที่ 1 2 3 4 5 6 7 8 9 10 11 12 13 รวม

ชดุ A : ∑1 =31 =

2 ∑ 1 =31 2 =

15.2.1.1) หาพสิ ัย (R) ของข้อมูลชุด A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.2.1.2) พสิ ัยระหวา่ งควอรไ์ ทล์ (IQR) ของข้อมูลชดุ A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

บทท่ี 3 : การวเิ คราะห์และนาเสนอข้อมูลเชงิ ปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 160

15.2.1.3) ส่วนเบ่ียงเบนมาตรฐาน (s) ของขอ้ มลู ชดุ A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.2.1.4) หาความแปรปรวน ( 2) ของข้อมูลชุด A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.2.2 หาพิสยั พิสัยระหวา่ งควอรไ์ ทล์ ส่วนเบย่ี งเบนมาตรฐาน และความแปรปรวน ของขอ้ มูลชดุ B ท่ีมีจานวน

ข้อมูล = ………………………. ข้อมูล

ตาแหนง่ ที่ 1 2 3 4 5 6 7 8 9 10 11 รวม

ชุด B : ∑1 =11 =

2 ∑1 =11 2 =

15.2.2.1) หาพิสยั (R) ของขอ้ มูลชุด B
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.2.2.2) พิสัยระหว่างควอร์ไทล์ (IQR) ของข้อมูลชดุ B
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.2.2.3) ส่วนเบ่ียงเบนมาตรฐาน (s) ของขอ้ มูลชุด B
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

บทที่ 3 : การวิเคราะห์และนาเสนอขอ้ มลู เชิงปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 161

15.2.2.4) หาความแปรปรวน ( 2) ของข้อมูลชุด B
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.2.3 หาพสิ ยั พิสัยระหว่างควอร์ไทล์ ส่วนเบีย่ งเบนมาตรฐาน และความแปรปรวน ของขอ้ มูลชุด C ท่ีมีจานวน

ขอ้ มลู = ………………………. ข้อมลู

ตาแหน่งที่ 1 2 3 4 5 รวม

ชุด C : ∑ 5 =1 =

2 ∑ 5 =1 2 =

15.2.3.1) หาพสิ ัย (R) ของข้อมูลชุด C
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.2.3.2) พิสัยระหว่างควอรไ์ ทล์ (IQR) ของขอ้ มลู ชุด C
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

15.2.3.3) ส่วนเบี่ยงเบนมาตรฐาน (s) ของขอ้ มูลชุด C
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ..............................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ..............................................................................................................................................................................................................................................................................................................................................................

15.2.2.4) หาความแปรปรวน ( 2) ของขอ้ มูลชดุ C
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

บทที่ 3 : การวเิ คราะหแ์ ละนาเสนอข้อมูลเชงิ ปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 162

15.3) ขอ้ มลู ชุดท่ีมกี ารกระจายมากทส่ี ุด

ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

16. ศิริวิทย์ไดร้ ับผลการสอบวชิ าภาษาไทย คณิตศาสตร์ ภาษาองั กฤษ และคอมพวิ เตอร์ พบวา่
- คา่ เฉล่ียเลขคณติ ของคะแนนสอบวชิ าคณติ ศาสตร์ และวิชาภาษาไทยเท่ากับ 21.5 คะแนน และ
- คา่ เฉลย่ี เลขคณิตของคะแนนสอบวชิ าภาษาองั กฤษ และวิชาคอมพิวเตอร์เท่ากบั 28.5 คะแนน
จงหาค่าเฉลยี่ เลขคณิตของคะแนนสอบทัง้ ส่ีวิชาน้ี

ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
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. ....................................................................................................................................................................................................................................................................................................................................................................
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. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

บทท่ี 3 : การวเิ คราะหแ์ ละนาเสนอขอ้ มลู เชิงปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 163

17. ถ้าค่าเฉล่ียเลขคณิตของอายุนักเรียนช้ันมัธยมศึกษาปีที่ 3 , 4 และ 5 ของโรงเรียนแห่งหน่ึงเท่ากับ 15 , 17
และ 18 ปีตามลาดับ และจานวนนักเรียนช้ันมัธยมศึกษาปีที่ 3 , 4 และ 5 ของโรงเรียนแห่งนี้เท่ากับ 60 , 50 และ 40
คนตามลาดบั จงหาคา่ เฉลยี่ เลขคณติ ของอายนุ ักเรยี นชั้นมธั ยมศกึ ษาปีที่ 3 – 5 ของโรงเรียนแห่งนี้

ตอบ∎ ............................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
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. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

18. นักเรียนช้นั มธั ยมศึกษาปที ี่ 6 คนหน่งึ ไดร้ ับใบรายงานผลการเรียนภาคเรยี นสุดท้าย ดงั น้ี

รหสั วชิ า ช่ือวิชา หน่วยกติ คะแนน เกรด

สาระการเรยี นรู้พื้นฐาน 3.5
3
ท33102 ภาษาไทย 6 1.0 78 4
4
ค33102 คณติ ศาสตร์ 6 1.0 70 3
2.5
ส33103 สงั คมศึกษา 6 0.5 82 4

ส33104 พระพทุ ธศาสนา 6 0.5 85 3.5
2
ศ33101 ศิลปะ 5 0.5 74 4
4
ง33102 เครอื ขา่ ยและโครงงานคอมพวิ เตอร์ 0.5 68 4
3.5
อ33102 ภาษาอังกฤษ 6 1.0 87 4
4
สาระการเรียนรเู้ พมิ่ เติม

ท30206 เสรมิ ทักษะภาษาไทย 2 1.0 76

ว30282 วิทยาศาสตรเ์ พม่ิ เตมิ 2 0.5 63

พ33201 ชีวติ กบั สขุ ภาพ 3 0.5 88

พ33202 กฬี ากบั สขุ ภาพ 3 0.5 90

ญ33202 ภาษาญ่ปี ุ่น 6 3.0 87

อ30206 ภาษาองั กฤษเพ่อื การสื่อสาร 6 0.5 79

อ33205 ภาษาอังกฤษเพอ่ื การอา่ น-เขียน 6 1.0 84

อ33206 ภาษาองั กฤษรอบรู้ 6 1.0 82

บทท่ี 3 : การวเิ คราะห์และนาเสนอขอ้ มลู เชิงปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 164

18.1) จงหาเกรดเฉล่ยี ของภาคเรียนสุดท้ายของนกั เรยี นคนน้ี
18.2) ถา้ นักเรยี นคนน้ีมีหนว่ ยกิตสะสมและเกรดเฉล่ยี ของ 5 ภาคเรียนที่ผ่านมา เปน็ 75.0 หน่วยกิต และ 3.75

ตามลาดบั จงหาเกรดเฉล่ียของทงั้ 6 ภาคเรียนของนักเรยี นคนนี้
วิธีทา จากโจทย์นาขอ้ มลู มาหาคา่ เฉลย่ี เลขคณิตถว่ งนา้ หนกั ไดด้ งั นี้

รหัสวิชา ชอ่ื วิชา หน่วยกติ ( ) คะแนน เกรด ( )
∑ =1 =
ท33102 สาระการเรยี นรพู้ นื้ ฐาน 1.0 78 3.5
ค33102 1.0 70 3
ส33103 ภาษาไทย 6 0.5 82 4
ส33104 คณิตศาสตร์ 6 0.5 85 4
ศ33101 สังคมศกึ ษา 6 0.5 74 3
ง33102 พระพุทธศาสนา 6 0.5 68 2.5
อ33102 ศิลปะ 5 1.0 87 4
เครอื ข่ายและโครงงานคอมพิวเตอร์
ท30206 ภาษาอังกฤษ 6 1.0 76 3.5
ว30282 0.5 63 2
พ33201 สาระการเรยี นรู้เพิ่มเตมิ 0.5 88 4
พ33202 0.5 90 4
ญ33202 เสริมทกั ษะภาษาไทย 2 3.0 87 4
อ30206 วิทยาศาสตร์เพิ่มเตมิ 2 0.5 79 3.5
อ33205 ชีวิตกบั สขุ ภาพ 3 1.0 84 4
อ33206 กีฬากับสุขภาพ 3 1.0 82 4
ภาษาญป่ี ่นุ 6 ∑ =1 =
ภาษาอังกฤษเพอ่ื การสือ่ สาร 6
ภาษาอังกฤษเพอ่ื การอา่ น-เขยี น 6
ภาษาอังกฤษรอบรู้ 6

รวม

18.1) จงหาเกรดเฉล่ียของภาคเรียนสุดท้ายของนักเรยี นคนนี้

ตอบ∎ .....................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
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18.2) ถ้านกั เรียนคนนมี้ ีหนว่ ยกติ สะสมและเกรดเฉลยี่ ของ 5 ภาคเรียนที่ผ่านมา เปน็ 75.0 หน่วยกิต และ 3.75

ตามลาดับ จงหาเกรดเฉล่ียของท้งั 6 ภาคเรยี นของนักเรียนคนน้ี

ตอบ∎ .....................................................................................................................................................................................................................................................................................................................................
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บทท่ี 3 : การวิเคราะห์และนาเสนอขอ้ มูลเชงิ ปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 165

19. ข้อมูลชุดหน่ึงประกอบด้วยจานวนเต็ม 5 จานวน โดยค่าเฉล่ียเลขคณิตของข้อมูลชุดนี้เท่ากับ 360 เม่ือเรียงข้อมูล
จากมากไปน้อยปรากฏวา่ ขอ้ มูล 2 ตัวสดุ ท้ายคอื 102 และ 99 ตามลาดับ จงหาคา่ ทีม่ ากท่ีสุดท่ีเป็นไปไดข้ องข้อมูลชดุ นี้

ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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20. ข้อมูลชุดหน่ึงประกอบด้วยจานวนเต็ม 5 จานวน โดยค่าเฉลี่ยเลขคณิตมัธยฐาน ฐานนิยม และพิสัย ของ
ข้อมูลชุดน้เี ทา่ กบั 5 จงหาชดุ ของข้อมลู ทีเ่ ปน็ ไปไดท้ งั้ หมด

ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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. ....................................................................................................................................................................................................................................................................................................................................................................

บทท่ี 3 : การวเิ คราะหแ์ ละนาเสนอขอ้ มูลเชิงปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 166

21. ร้านค้าแห่งหน่ึงต้องการวิเคราะห์ข้อมูลการขายสินค้าของร้านจึงได้บันทึกจานวนสินค้า (ช้ิน) ท่ีขายได้ในหน่ึงวันโดย
ร่วมเก็บขอ้ มูลเพียง 11 วัน ในหนงึ่ เดอื นท่ีผา่ นมาได้ขอ้ มูลดังนี้

85 125 30 75 80 65 90 75 78 92 67

21.1)จงหาควอรไ์ ทลท์ ี่ 1 ควอร์ไทลท์ ี่ 2 และควอรไ์ ทลท์ ่ี 3 ของข้อมูลชุดน้ี
21.2)จงหาพิสัยและพิสัยระหว่างควอร์ไทล์ของข้อมูลชุดนี้ และพิจารณาว่าค่าวัดการกระจายสัมบูรณ์ใดเหมาะ
สาหรับใชอ้ ธิบายลักษณะการกระจายของขอ้ มลู น้พี ร้อมทั้งใหเ้ หตุผลประกอบ
21.3)จงหาเปอร์เซน็ ไทล์ที่ 25 เปอรเ์ ซน็ ไทลท์ ่ี 50 เปอร์เซน็ ไทล์ที่ 75 และเปอร์เซน็ ไทลท์ ี่ 90 ของขอ้ มูลชดุ นี้
วิธีทา 21.1) จงหาควอรไ์ ทลท์ ่ี 1 ควอรไ์ ทล์ท่ี 2 และควอร์ไทล์ท่ี 3 ของขอ้ มลู ชุดนี้ โดยเรยี งคา่ ของข้อมูลตามตาแหนง่ ท่ี

ของขอ้ มูลจากนอ้ ยไปหามาก จากโจทย์ จานวนขอ้ มูลชุดน้ี มี วนั = ....................................

ตาแหน่งท่ี 1 2 3 4 5 6 7 8 9 10 11
คะแนน ( )

( ) ( )21.1.1) หาค่าตา่ สุด ของข้อมูล คือ ......................................... หาค่าสูงสุด ของข้อมลู คือ .........................................

21.1.2) หา 1 , 2 และ 3 หาได้จากสูตร ตาแหน่งควอไทล์ที่ = ( +1) เม่อื จานวนข้อมลู = ……………. ดังนี้
4

อยใู่ นตาแหนง่ ที่21.1.2.1) 1 ............................................................................................................................................................................................................................................

ดังน้นั ค่าของ 1 = ...........................................................................................................................................................................................................................................

อยใู่ นตาแหน่งที่21.1.2.2) 2 ............................................................................................................................................................................................................................................

ดังนน้ั คา่ ของ 2 = ......................................................................................................................................................................................................................................

อยู่ในตาแหนง่ ท่ี21.1.2.3) 3 .........................................................................................................................................................................................................................................

ดังนั้นค่าของ 3 = ....................................................................................................................................................................................................................................
21.1.3) ข้อมลู ชุดนมี้ ีคา่ นอกเกณฑห์ รอื ไม่ถา้ มคี อื คา่ ใด : หาค่านอกเกณฑ์

หาคา่21.1.3.1) 1 − 1.5( 3 − 1) = ................................................................................................................................................................................

= ................................................................................................................................................................................

หาค่า21.1.3.2) 3 + 1.5( 3 − 1) = ..................................................................................................................................................................................

= ................................................................................................................................................................................

จะพบว่า มขี อ้ มลู ที่นอ้ ยกว่า ไดแ้ ก่ 1 − 1.5( 3 − 1) .............................................................................................................................................................................

และ มขี อ้ มูลทีม่ ากกว่า ได้แก่ 3 + 1.5( 3 − 1) ...........................................................................................................................................................................

ดังนั้น ค่านอกเกณฑข์ องข้อมูลชุดน้ี ไดแ้ ก่ .....................................................................................................................................................................................................................

บทที่ 3 : การวิเคราะหแ์ ละนาเสนอข้อมลู เชงิ ปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 167

21.1.3) เขียนแผนภาพกล่อง (Box plot) เพอื่ นาเสนอขอ้ มลู ชุดนี้

∎ สรุปขอ้ มูลทไ่ี ด้จากแผนภาพกลอ่ ง

21.2)จงหาพิสัย และพิสัยระหว่างควอร์ไทล์ ส่วนเบ่ียงเบนมาตรฐาน และความแปรปรวน ของข้อมูลชุดน้ี และ
พิจารณาว่าค่าวัดการกระจายสัมบูรณ์ใดเหมาะสาหรับใช้อธิบายลักษณะการกระจายของข้อมูลน้ีพร้อมทั้งให้เหตุผล
ประกอบ

ในทน่ี ีจ้ ะหา พสิ ัย พสิ ยั ระหว่างควอร์ไทล์ ส่วนเบ่ยี งเบนมาตรฐาน และความแปรปรวน ของขอ้ มูล ทมี่ ีจานวนขอ้ มูล
= ………………………………. ข้อมลู

ตาแหนง่ ท่ี 1 2 3 4 5 6 7 8 9 10 11 รวม

ชุด A : ∑1 =61 =

2 ∑ 1 =61 2 =

21.2.1) หาพสิ ยั (R) ของขอ้ มูลชดุ A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

21.2.1) พสิ ัยระหว่างควอร์ไทล์ (IQR) ของข้อมลู ชุด A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

21.2.3) ส่วนเบี่ยงเบนมาตรฐาน (s) ของขอ้ มลู ชุด A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

บทท่ี 3 : การวิเคราะห์และนาเสนอขอ้ มูลเชงิ ปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 168

21.2.4) หาความแปรปรวน ( 2) ของขอ้ มลู ชดุ A
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

21.2.5) พิจารณาว่าค่าวัดการกระจายสัมบูรณ์ใดเหมาะสาหรับใช้อธิบายลักษณะการกระจายของข้อมูลนี้พร้อม
ทง้ั ใหเ้ หตผุ ลประกอบ

จากการหา พิสัย พิสัยระหว่างควอร์ไทล์ ส่วนเบี่ยงเบนมาตรฐาน และความแปรปรวน ของข้อมูลข้างต้น (ข้อ
21.2.1 - 21.2.4) สามารถสรุปไดว้ า่ ค่าวดั การกระจายทเ่ี หมาะสาหรบั ใชอ้ ธิบายลกั ษณะการกระจายของขอ้ มูลชุดนี้ คอื
ตอบ.∎ ..............................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

21.3)จงหาเปอร์เซ็นไทล์ที่ 25 เปอร์เซ็นไทล์ท่ี 50 เปอร์เซ็นไทล์ที่ 75 และเปอร์เซ็นไทล์ท่ี 90 ของข้อมูลชุดนี้
โดยเรียงคา่ ของขอ้ มลู ตามตาแหนง่ ท่ขี องข้อมลู จากน้อยไปหามาก

ตาแหน่งที่ 1 2 3 4 5 6 7 8 9 10 11
คะแนน ( )

( ) ( )21.3.1) หาค่าตา่ สุด ของขอ้ มูล คือ ......................................... หาคา่ สงู สุด ของข้อมลู คือ .........................................

21.3.2) หา 25 , 50 , 75 และ 90 หาได้จากสูตร ตาแหน่งเปอร์เซนไทลท์ ่ี = ( +1)
100

เม่ือจานวนข้อมลู = ………………..……. ดังนี้

อยู่ในตาแหนง่ ท่ี21.3.2.1) 25 ...............................................................................................................................................................................................................................................................

ดังนัน้ ค่าของ 25 = ................................................................................................................................................................................................................................. ... ∎

อย่ใู นตาแหนง่ ที่21.3.2.2) 50 ...............................................................................................................................................................................................................................................................

ดังนนั้ คา่ ของ 50 = ................................................................................................................................................................................................................................. ... ∎

อยู่ในตาแหน่งท่ี21.3.2.3) 75 ..............................................................................................................................................................................................................................................................

ดงั น้ันค่าของ 75 = ................................................................................................................................................................................................................................. ... ∎

อยใู่ นตาแหน่งที่21.3.2.4) 90 ...............................................................................................................................................................................................................................................................

ดงั นัน้ ค่าของ 90 = ................................................................................................................................................................................................................................ ... ∎

บทท่ี 3 : การวเิ คราะห์และนาเสนอข้อมูลเชิงปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 169

22. ความสงู (เซนติเมตร) ของนกั กฬี าบาสเกตบอลชายและหญิงของโรงเรยี นแห่งหนงึ่ ซ่งึ มจี านวนทง้ั หมด 40 คน

โดยเรยี งข้อมูลจากนอ้ ยไปมากแสดงไดด้ งั นี้

นกั กฬี าบาสเกตบอลชาย

175 176 179 180 180
180 181 183 185 188
189 190 190 195 195
195 196 198 198 206

นกั กฬี าบาสเกตบอลหญงิ

153 154 157 160 161
163 166 167 168 168
168 170 171 171 172
172 174 175 181 182

22.1) จงเขยี นแผนภาพลาต้นและใบเพือ่ นาเสนอข้อมูลสองชุดนใี้ นแผนภาพเดียวกัน
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ..................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

22.2) จากแผนภาพในขอ้ 22.1) ควรใชค้ ่ากลางใด เป็นตวั แทนของขอ้ มูลแต่ละชุด เพราะเหตุใด
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

22.3) นกั กีฬาบาสเกตบอลชายท่ีสูงมากกว่าค่าเฉลี่ยเลขคณิตคดิ เป็นรอ้ ยละเทา่ ใดของจานวนนกั กีฬบาสเกตบอล
ชายทง้ั หมด
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

บทที่ 3 : การวิเคราะห์และนาเสนอข้อมูลเชิงปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 170

23. เวลา (นาท)ี ที่ใชใ้ นการอ่านหนังสอื ในวนั หนง่ึ ของนักเรียน 2 หอ้ งเรียนท่ีสุ่มมาจานวนหอ้ งละ 10 คน แสดงได้ดงั น้ี

ห้อง 1 0 20 30 42 35 82 54 28 0 63
ห้อง 2 45 40 62 10 24 15 30 60 95 120

จงหาสัมประสิทธ์ิการแปรผันของเวลาที่ใช้ในการอ่านหนังสือในหน่ึงวันข องนักเรียนแต่ละห้องท่ีสุ่มมาพร้อมทั้ง

เปรยี บเทียบการกระจายของเวลาท่ีใช้ในการอา่ นหนังสอื ในหนึ่งวันของนักเรยี นทง้ั สองห้อง

วิธีทา จากโจท์สร้างตารางข้อมูลเพ่ือหา สัมประสิทธ์ิการแปรผัน (C.V. = ) โดยหาค่าเฉล่ียเลขคณิตและส่วนเบี่ยงเบน
| |

มาตรฐาน ของแตล่ ะหอ้ ง ซง่ึ แต่ละห้องมจี านวนนกั เรยี น คน = ......................................

หอ้ ง 1 ( ) 0 20 30 42 35 82 54 28 0 63 ∑ 1 =01 =
2 ∑1 =01 2 =

ห้อง 2 ( ) 45 40 62 10 24 15 30 60 95 120 ∑ 1 =01 =
2 ∑ 1 =01 2 =

23.1) หาสมั ประสทิ ธก์ิ ารแปรผนั ของเวลาที่ใช้ 23.2) หาสัมประสทิ ธกิ์ ารแปรผันของเวลาที่ใช้
อ่านหนงั สือของนักเรียนห้อง 1 อา่ นหนังสือของนกั เรียนห้อง 2

ก) หาค่าเฉลย่ี ของเวลาทีใ่ ช้อา่ นหนังสอื ( ) นาที ก) หาค่าเฉลยี่ ของเวลาท่ีใชอ้ า่ นหนงั สอื ( ) นาที

= ∑ =1 = ∑ =1



=. . =. .

นาที= ……………………………………. ∎ นาที= ……………………………………. ∎

ข) หาส่วนบยี่ งเบนมาตรฐานของเวลาท่ใี ช้อ่านหนงั สือ( ) ข) หาส่วนบี่ยงเบนมาตรฐานเวลาทีใ่ ช้อ่านหนังสือ ( )

= √∑ =1 2 − ̄ 2 = √∑ =1 2 − ̄ 2

−1 −1

= ………………………………………………………………………… = …………………………………………………………………………

= ……………………………………………….………………………… = ……………………………………………….…………………………

= นาที……………………………………………………………………….… ∎ = นาที……………………………………………………………………….… ∎

ค) หาสัมประสทิ ธ์ิการแปรผันของเวลาท่ีใช้อา่ นหนงั สือ ค) หาสมั ประสิทธกิ์ ารแปรผันของเวลาทใ่ี ชอ้ า่ นหนังสือ

จะได้ (C. V. ) = จะได้ (C. V. ) =
| ̄ | | ̄ |
. .
=. =.

= ……………………………. ∎ = ……………………………. ∎

จากการเปรียบเทยี บการกระจายโดยใช้สมั ประสิทธข์ิ องการแปรผนั (C.V.) สรุปได้ว่า
∎ ตอบ

บทท่ี 3 : การวเิ คราะหแ์ ละนาเสนอข้อมลู เชงิ ปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 171

24. อรรถฤทธ์ิได้สารวจจานวนลูกเกดที่ใส่ในขนมปังแต่ละอันท่ีซื้อจากร้านขายขนมปัง 2 แห่ง และนาเสนอด้วยแผนภาพกล่อง
ดังน้ี

รา้ นที่ 1

ร้านท่ี 2

24 25 26 27 28 29 30 31 32 33 34 35 36

24.1) จงหามธั ยฐานของจานวนลูกเกดท่ใี สใ่ นขนมปงั แตล่ ะอนั แต่ละร้าน
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

24.2) ขนมปังจากร้านท่ี 1 ท่ีมีจานวนลูกเกดน้อยกว่า 31 เม็ด คิดเป็นร้อยละเท่าใดของจานวนขนมปังที่ซ้ือจาก
รา้ นท่ี 1 ทัง้ หมด
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

24.3) จงหาควอร์ไทล์ท่ี 3 ของจานวนลูกเกดทใี่ ส่ในขนมปงั แต่ละอันท่ซี อ้ื จากร้านท่ี 2
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

24.4) ถ้าอรรถฤทธิ์ ต้องการซ้ือขนมปังลกู เกดมาขายเขาควรซ้อื ขนมปังลกู เกดจากรา้ นใดจงึ จะมีโอกาสได้ลูกเกด
ในขนมปงั แต่ละอันใกลเ้ คยี งกนั เพราะเหตุใด
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

24.5) ถา้ อรรถฤทธช์ิ อบรับประทานลูกเกด เขาควรซ้ือขนมปังจากร้านใด จงึ จะมีโอกาส ไ ด้ ข น ม ปั ง ท่ี มี ลู ก เ ก ด
มากกวา่ เพราะเหตุใด
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................

บทที่ 3 : การวเิ คราะห์และนาเสนอขอ้ มลู เชงิ ปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 172

25. มานี ชูใจ และปิติ ได้ค่าขนมจากผู้ปกครอง โดยค่าเฉลี่ยเลขคณิตและส่วนเบ่ียงเบนมาตรฐานของค่าขนมของท้ัง
สามคนเทา่ กบั 50 และ 0 บาท ตามลาดบั ถา้ นาคา่ ขนมของมานะมาคานวณดว้ ยจะไดค้ า่ เฉลยี่ เลขคณติ ใหม่เปน็ 45 บาท

จงหาสว่ นเบยี่ งเบนมาตรฐาน ของค่าขนมของท้ังสี่คน

ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
. ....................................................................................................................................................................................................................................................................................................................................................................
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26. กาหนดใหข้ ้อมลู ของประชากรจานวน 2 ชดุ มีลักษณะดังต่อไปน้ี
ชุด A : ประกอบด้วยจานวนเตม็ ทแี่ ตกตา่ งกนั 5 จานวน โดยทงั้ 5 จานวนน้อี ยรู่ ะหว่าง 0 และ 10
ชุด B : ประกอบดว้ ยจานวนเตม็ ทแี่ ตกต่างกนั 5 จานวน โดยท้งั 5 จานวนนอ้ี ยู่ระหว่าง 10 และ 20

26.1) จงยกตวั อยา่ งข้อมูลชุด A และ B ทสี่ ่วนเบ่ียงเบนมาตรฐานของขอ้ มูลชุด A มากกวา่
ส่วนเบ่ยี งเบนมาตรฐานของข้อมูลชดุ B

ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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บทที่ 3 : การวเิ คราะหแ์ ละนาเสนอขอ้ มลู เชิงปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 173

26.2) มีโอกาสทส่ี ่วนเบยี่ งเบนมาตรฐานของข้อมลู แต่ละชดุ จะเป็น 0 หรอื ไมเ่ พราะเหตุใด

ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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26.3) จงยกตวั อย่างข้อมูลชุด A และ B ทส่ี ว่ นเบยี่ งเบนมาตรฐานของขอ้ มูลชุด A เทา่ กบั ส่วนเบย่ี งเบนมาตรฐาน
ของข้อมลู ชดุ B

ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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27. กาหนดข้อมูลของประชากรชดุ หนึ่งเรยี งลาดบั จากนอ้ ยไปมาก ได้ดังน้ี

1 2 3 3 6

ถ้าคา่ เฉล่ยี เลขคณิต และส่วนเบยี่ งเบนมาตรฐาน ของขอ้ มลู ชดุ น้ีเท่ากบั 3 และ 4√7 ตามลาดบั
7

จงหา และ
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บทท่ี 3 : การวิเคราะหแ์ ละนาเสนอข้อมูลเชิงปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 174

28. ข้อมลู ของตวั อย่างชุดหนง่ึ ที่ 20 ตัวโดยคา่ เฉลีย่ เลขคณิตและส่วนเบีย่ งเบนมาตรฐานของข้อมลู ชุดนี้ เท่ากับ 10 และ
2 ตามลาดับ ถ้าภายหลังพบว่ามีการบันทึกข้อมูลตัวหนึ่งผิดพลาดไปจาก 12 บันทึกผิด เป็น 8 จงหาค่าเฉล่ียเลขคณิต
และและความแปรปรวนทถ่ี ูกตอ้ งของข้อมูลชุดนี้

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29. จงพจิ ารณาวา่ ขอ้ สรุปตอ่ ไปน้ีถูกตอ้ งหรือไม่ พรอ้ มท้งั ใหเ้ หตุผลประกอบ

29.1) ถา้ คะแนนสอบของสมชายตรงกบั 30 แลว้ สมชายสอบได้ 30 % ของคะแนนเต็ม
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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29.2) ถ้าคะแนนสอบของสมหญิงตรงกับ 40 แล้วจะมีนกั เรียนสอบไดค้ ะแนนมากกวา่ สมหญิงอยู่ 60 คน
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บทท่ี 3 : การวิเคราะห์และนาเสนอขอ้ มลู เชงิ ปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 175

30. ขอ้ สอบวิชาหนง่ึ มีคะแนนเตม็ 80 คะแนนโดยคะแนนของผเู้ ขา้ สอบ 10 คน แสดงไดด้ งั น้ี

25 62 59 38 38 41 69 72 26 44

30.1) ถา้ เกณฑใ์ นการสอบผา่ นคือตอ้ งไดค้ ะแนนไมต่ า่ กวา่ รอ้ ยละ 70 ของคะแนนเตม็
จงหาคะแนนต่าสุดของผ้ทู ่สี อบผ่าน

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30.2) ถา้ เกณฑ์ในการสอบผา่ นคอื ตอ้ งได้คะแนนไมต่ า่ กว่าเปอรเ์ ซ็นไทลท์ ่ี 70
จงหาคะแนนตา่ สุดของผทู้ ่สี อบผา่ น

วิธที า หาค่าเปอร์เซ็นไทล์ท่ี 70 ( 70) โดยเรียงข้อมูลจากนอ้ ยไปหามาก

ตาแหนง่ ที่ 1 2 3 4 5 6 7 8 9 10
คะแนน

30.2.1) หา 70 หาได้จากสตู ร ตาแหนง่ เปอร์เซนไทล์ท่ี = ( +1) เม่ือจานวนข้อมูล = ………………..……. ดังนี้

100

ค่า อยใู่ นตาแหน่งที่30.2.2) 70 ............................................................................................................................................................................................................................................

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ดังนั้นค่าของ 70 = ........................................................................................................................................................................................................................................................

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นน่ั คือเกณฑ์ในการสอบผ่านคือตอ้ งได้คะแนนไม่ต่ากวา่ เปอร์เซน็ ไทล์ท่ี 70 ตรงกบั คะแนนขั้นตา่ ที่เท่ากับ ........................... คะแนน ∎

บทที่ 3 : การวเิ คราะหแ์ ละนาเสนอขอ้ มลู เชงิ ปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 176

31. ปรมิ าณน้าฝน (มิลลเิ มตร) ของจงั หวดั ในภาคเหนอื ในเดอื นสิงหาคม พ.ศ. 2556 แสดงได้ดังนี้

จงั หวัด ปรมิ าณน้าฝน (มิลลิเมตร)

กาแพงเพชร 214.2

เชียงใหม่ 299.4

เชียงราย 423.2

ตาก 112.2

นครสวรรค์ 84.0

นา่ น 224.7

เพชรบรู ณ์ 164.0

แพร่ 365.2

พะเยา 229.1

พิษณโุ ลก 197.5

แมฮ่ ่องสอน 320.6

ลาปาง 220.9

ลาพนู 142.5

อตุ รดติ ถ์ 392.4

จงหา

31.1) ปริมาณน้าฝนท่ีมีจังหวัดในภาคเหนือประมาณร้อยละ 87 มีปรมิ าณน้าฝนนอ้ ยกวา่

วิธที า เนือ่ งจากปริมาณน้าฝนทมี่ ีจงั หวดั ในภาคเหนือประมาณร้อยละ 87

จะตรงกบั คา่ ที่น้อยกวา่ คา่ เปอรเ์ ซนไทล์ท่ี 87 ( 87) ดงั นน้ั ต้องเรยี งขอ้ มูลจากน้อยไปหามาก

ตาแหนง่ ที่ จงั หวดั ปรมิ าณนา้ ฝน (มลิ ลเิ มตร)

1
2
3
4
5
6
7
8
9
10
11
12
13
14

บทที่ 3 : การวเิ คราะห์และนาเสนอขอ้ มูลเชิงปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 177

∎ ตอบ 31.1.1) หา 87 หาได้จากสูตร ตาแหน่งเปอร์เซนไทลท์ ี่ = ( +1) เมอ่ื จานวนขอ้ มูล = ………………..……. ดังน้ี
100
ค่า อย่ใู นตาแหนง่ ท่ี31.1.2) 87
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ดังนนั้ ค่าของ 87 .............................................................................................................................................................................................................................................................................................................

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31.2) ปริมาณนา้ ฝนทมี่ ีจังหวดั ในภาคเหนือประมาณรอ้ ยละ 60 มีปริมาณน้าฝนมากกว่า

∎ ตอบ เนอื่ งจากปริมาณน้าฝนที่มีจังหวัดในภาคเหนือประมาณร้อยละ 60 มีปริมาณน้าฝนมากกว่า จะตรงกับคา่

ทมี่ ากกว่าค่าเปอรเ์ ซนไทล์ท่ี 60 พจิ ารณาการเรียงลาดับตาแหนง่ ทข่ี องข้อมูลจากตารางขา้ งต้น จะไดว้ า่

เราจะต้อง

31.2.1) หา 60 หาได้จากสตู ร ตาแหน่งเปอร์เซนไทล์ท่ี = ( +1) เมือ่ จานวนข้อมลู = ………………..……. ดังน้ี

ค่า อยใู่ นตาแหนง่ ท่ี31.2.2) 60 100

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ดงั นัน้ คา่ ของ 60 ..............................................................................................................................................................................................................................................................................................................

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บทที่ 3 : การวิเคราะหแ์ ละนาเสนอขอ้ มลู เชิงปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 178

32. ผลการทดสอบความสามารถในการคิดอย่างมีวิจารณญาณของนักเรียนช้ันมัธยมศึกษาปีที่ 6 ของโรงเรียนแห่งหนึ่ง
จานวนทั้งหมด 40 คนซ่ึงมีคะแนนเตม็ 100 คะแนน โดยเรียงคะแนนจากน้อยไปมาก แสดงได้ดงั น้ี

43 45 48 49 50 51 53 54 54 54
55 56 56 58 60 60 62 63 65 65
65 66 67 69 74 75 76 76 77 78
78 80 82 84 85 92 94 96 97 98

32.1) จงหาคะแนนทมี่ นี ักเรียนประมาณคร่ึงหนึง่ ของช้ันไดค้ ะแนนต่ากว่า 7 8 9 10
วธิ ที า เรยี งขอ้ มูลจากนอ้ ยไปหามาก

ตาแหน่งที่ 1 2 3 4 5 6
คะแนน

ตาแหน่งท่ี 11 12 13 14 15 16 17 18 19 20
คะแนน

ตาแหนง่ ที่ 21 22 23 24 25 26 27 28 29 30
คะแนน

ตาแหน่งท่ี 31 32 33 34 35 36 37 38 39 40
คะแนน

∎ ตอบ หาคะแนนท่ีมนี ักเรียนประมาณครึ่งหนง่ึ ของชั้นได้คะแนนตา่ กว่า
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32.2) จงหาคะแนนที่มนี ักเรียนประมาณหนึง่ ในสี่ของชน้ั ไดค้ ะเเนนสงู กว่า
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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บทที่ 3 : การวิเคราะหแ์ ละนาเสนอขอ้ มลู เชงิ ปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 179

32.3) จงหาคะแนนที่มีนักเรียนประมาณหกในสบิ ของชน้ั ไดค้ ะแนนต่ากวา่

ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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32.4) ถ้าโรงเรียนแห่งน้ีจัดกิจกรรมพัฒนาทักษะการคิดอย่างมีวิจารณญาณให้กับนักเรียนท่ีได้คะแนนน้อยกว่า

เปน็ วา่ เปอรเ์ ป็นไทลท์ ่ี 25 จงหาจานวนนักเรียนที่ต้องเขา้ ร่วมกจิ กรรมนี้

ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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บทที่ 3 : การวเิ คราะหแ์ ละนาเสนอขอ้ มลู เชงิ ปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 180

33. อตั ราเรว็ สูงสดุ ในการเคลื่อนท่ี (ไมลต์ ่อชั่วโมง) ของสัตวป์ ่าและสตั ว์เลี้ยง แสดงด้วยแผนภาพกล่อง ไดด้ งั นี้

สตั วป์ ่า

สตั วเ์ ลย้ี ง x

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74

33.1) จงหามัธยฐานและค่าสูงสุดของอตั ราสงู สดุ ในการเคล่อื นท่ขี องสตั วป์ ่าและสตั วเ์ ลี้ยง
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33.2) จงว่าพสิ ัยระหว่างควอร์ไทลข์ องอัตราเร็วสงู สุด ในการเคล่ือนที่ของสัตว์ปา่ และสัตว์เลยี้ ง
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33.3) สามารถสรุปได้หรือไม่ว่าสัตว์ป่าส่วนใหญ่มีอัตราเร็วสูงสุดในการเคลื่อนท่ีน้อยกว่า 49 ไมล์ต่อชั่วโมง
เพราะเหตใุ ด
ตอบ∎ ................................................................................................................................................................................................................................................................................................................................................
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บทท่ี 3 : การวเิ คราะห์และนาเสนอข้อมลู เชงิ ปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 181

34. จานวนครั้งของการดาวนโ์ หลดแอบพลิเคชัน A และ B ตั้งแต่เดือนมกราคมถึงธนั วาคม พ.ศ. 2561
แสดงด้วยแผนภาพกลอ่ ง ไดด้ งั นี้

จานวนครัง้ ของการดาวน์โหลด
แอบพลเิ คชัน A

จานวนครัง้ ของการดาวน์โหลด
แอบพลิเคชัน B

40 80 120 160 200 240 280 320 360 400 440 480 520 560 600 640

34.1) จงเปรียบเทียบคา่ ตา่ สุดมัธยฐาน และค่าสงู สุดของจานวนคร้ังของการดาวนโ์ หลดแอปพลิเคชันทัง้ สอง
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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34.2) จงเปรียบเทียบพิสัยระหวา่ งควอร์ไทลข์ องจานวนครัง้ ของการดาวน์โหลดแอปพลเิ คชันทงั้ สอง
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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บทท่ี 3 : การวิเคราะหแ์ ละนาเสนอข้อมูลเชิงปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 182

35. สหประชาชาติ (United Nations: UN) เป็นองค์การระหว่างประเทศซ่ึงมีจุดมุ่งหมายในการรักษาสันติภาพและ
ความมั่นคงระหว่างประเทศ โดยทุกปีต้ังแต่ พ.ศ. 2555 สหประชาชาตจิ ะรายงานดัชนคี วามสุขของแต่ละประเทศในโลก
ซึ่งมีคะแนนตั้งแต่ 0 ถึง 10 ถ้าประเทศใดมีคะแนนมากหมายความว่า คนในประเทศนั้นมีความสุขมากจากรายงานชุดน้ี
ใน พ.ศ. 2560 ดัชนีความสุขของประเทศที่สุม่ มาจาก 3 ทวีป ทวีปละ 12 ประเทศแสดงได้ดงั ตารางตอ่ ไปน้ี

เอเชยี อเมริกา ยโุ รป

เกาหลีใต้ 5.838 สหรฐั อเมรกิ า 6.993 เบลเย่ยี ม 6.891
ไทย 6.424 แคนาดา 7.316 โครเอเชีย 5.293
จีน 5.273 เปรู 5.715 รัสเซีย 5.963
ญปี่ ่นุ 5.920 ชิลี 6.652 สหราชอาณาจักร 6.714
อนิ เดยี 4.315 เมก็ ซิโก 6.578 สโลวเี นีย 5.758
เมยี นมา 4.545 เวเนซเุ อลา 5.250 กรีซ 5.227
อนิ โดนเี ซีย 5.262 ปารากวัย 5.493 นอรเ์ วย์ 7.537
ปากีสถาน 5.269 กัวเตมาลา 6.454 ฝรัง่ เศส 6.442
ภูฎาน 5.011 อารเ์ จนตินา 6.599 สเปน 6.403
สงิ คโปร์ 6.572 เฮติ 3.603 เยอรมนี 6.951
อิหร่าน 4.692 เอลซัลวาดอร์ 6.003 อติ าลี 5.964
บงั กลาเทศ 4.608 ฮอนดูรัส 5.181 โปรตุเกส 5.195

จากขอ้ มลู ขา้ งตน้ สามารถเขียนแผนภาพกล่องแสดงดชั นีความสุขของประเทศท่ีส่มุ มาจากแตล่ ะทวปี ได้ ดังนี้

(1)

(2)

(3)

3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8

35.1) จงพจิ ารณาว่าแผนภาพกล่อง (1) , (2) และ (3) แสดงดัชนีความสขุ ของประเทศท่สี มุ่ มาจากทวปี ใด
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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บทที่ 3 : การวเิ คราะหแ์ ละนาเสนอขอ้ มูลเชงิ ปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 183

35.2) จงเปรยี บเทียบค่าต่าสดุ มัธยฐาน และค่าสูงสดุ ของดชั นีความสุข ของประเทศทส่ี มุ่ มาจากแต่ละทวีป

ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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35.3) ม่อื พจิ ารณาเฉพาะประเทศท่ีสุม่ มา ทวีปใดมกี ารกระจายของดัชนีความสุขมากท่สี ุด เพราะเหตุใด

ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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⊠ 35.4) โดยภาพรวม เม่ือพิจารณาเฉพาะประเทศที่สุ่มมาทวีปใดมีดัชนีความสุขมากท่ีสุด พร้อมทั้งให้เหตุผล
ประกอบ

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บทท่ี 3 : การวเิ คราะหแ์ ละนาเสนอขอ้ มลู เชงิ ปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 184

36. เพลงรพณิ ได้เข้าร่วมการทดสอบวัดผลวชิ าคณติ ศาสตร์ระดบั ประเทศ ทีจ่ ดั โดยสถาบนั แหง่ หนงึ่
และได้รบั ใบรายงานผลสอบ ดงั น้ี

ใบรายงานผลสอบ

ชอื่ เพลงรพิณ สกุล อินทรเศวต เลขประจาตัว 001123
จานวนผู้เข้าสอบทั้งหมด 621,519 คะแนนทีไ่ ด้ 28 คะแนนเตม็ 100
คดิ เป็นเปอรเ์ ปน็ ไทล์ที่ 90

ถา้ เพลงพิณปน็ ผเู้ ข้าสอบคนเดียวทไ่ี ด้ 28 คะแนน
36.1) สามารถสรุปไดห้ รือไมว่ า่ เพลงพิณได้คะแนนมากกวา่ ผู้เข้าสอบส่วนใหญ่
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36.2) ข้อสอบที่ใชใ้ นการวัดผลครัง้ น้ีน่าจะยากหรืองา่ ยเกินไปสาหรบั ผู้เขา้ สอบส่วนใหญ่เพราะเหตใุ ด
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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36.3) มผี เู้ ขา้ สอบประมาณกี่คนทีไ่ ดค้ ะแนนมากกวา่ เพลงรพิณ
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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36.4) เปน็ ไปไดห้ รือไม่ท่ีคะแมนเฉลี่ยของผเู้ ข้าสอบทัง้ 621,519 คนนม้ี ากกว่า 38 คะแนน เพราะเหตุใด
ตอบ∎ ..............................................................................................................................................................................................................................................................................................................................................
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บทท่ี 3 : การวิเคราะหแ์ ละนาเสนอข้อมลู เชงิ ปริมาณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 185

หนงั สอื อา้ งอิง

สถาบันสง่ เสรมิ การสอนวิทยาศาสตร์และเทคโนโลยี (สสวท.). 2563. หนังสอื เรียนรายวิชาคณติ ศาสตร์พนื้ ฐาน ชน้ั

มธั ยมศึกษาปีที่ 6 : กรุงเทพมหานคร พมิ พค์ รงั้ ที่ 1 โรงพิมพ์ สกสค. ลาดพร้าว, 203 หน้า.

แบบบันทึกคะแนนเกบ็ และคะแนนทดสอบเพ่อื ตดั สนิ ผลการเรยี น

ท่ี กิจกรรม ชื่อกิจกรรมท่ีปฏิบัตริ ะหว่างเรยี น คะแนนเตม็ คะแนนท่ีได้ ลงช่อื ครูผู้สอน ว/ด/ป

1 กก. 1

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รวมคะแนนงาน/กจิ กรรม/แบบฝกึ หัดระหว่างเรียน (50 คะแนน)

1 ทดสอบ ทดสอบยอ่ ย 1

2 ทดสอบ ทดสอบย่อย 2

3 ทดสอบ ทดสอบกลางภาค

4 ทดสอบ ทดสอบปลายภาค

รวมคะแนน 100

บทท่ี 3 : การวเิ คราะหแ์ ละนาเสนอข้อมูลเชงิ ปรมิ าณ MA33101- MA33102 M.6 PAKKRED SECONDARY SCHOOL : 186

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