Engineering Mathematics case study

DEPARTMENT OF MATHEMATICS, SCIENCE &
COMPUTER

DBM30033 : ENGINEERING MATHEMATICS III

CASE STUDY SET 3

LECTURER’S NAME:
PUAN HAZWANI BINTI BACHOK

PREPARED BY:

1. DARSHINI A/P MITHIVANAN 33DCE20F1007
2. KIRTHIKA A/P ANANDAN 33DCE20F1008
3. KARTHIGA A/P KALAISELVAN 33DCE20F1011
4. THIRUNAGGE SRI A/P RAMESH 33DCE20F1015

TABLE OF CONTENTS

1 Question 3
2 Introduction 4-5
6
3 Data 7
4 Frequency table 8-13
5 Measure of Central
14-17
Tendency & Dispersion
5.1 Mean 18-20
5.2 Median
5.3 Mode 21
22
5.4 Mean deviation
5.5 Variance & Standard Deviation

5.6 Percentile
6 Histogram & Ogive Graph

6.1 Histogram

6.1.1 Mode from Histogram

6.2 Ogive Graph

7 Measure Quartile & Decile
using Graph
7.1 First quartile
7.2 Third quartile
7.3 Interquartile range
7.4 Decile
- 3th decile

8 Discussion & Conclusion
9 References

1.0 QUESTION

3

2.0 INTRODUCTION

• Exports are goods and services that are
produced in one country and purchased by
the residents of another country. It doesn't
matter what the good or service is, or how
it's sent.

• A product can be shipped, sent by email, or
carried in personal luggage on a plane. It's
an export if it's produced domestically and
sold to someone in a foreign country. The
effects of this process can trickle down to
consumers.

• Statistics is a branch of applied
mathematics that involves the collection,
description, analysis, and inference of
conclusions from quantitative data.

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The two major areas of statistics are known as descriptive statistics, which describes the
properties of sample and population data, and inferential statistics, which uses those
properties to test hypotheses and draw conclusions
• Descriptive Statistics
Descriptive statistics mostly focus on the central tendency, variability, and distribution of
sample data. Central tendency means the estimate of the characteristics, a typical element of
a sample or population, and includes descriptive statistics such as mean, median, and mode.
• Inferential Statistics
Inferential statistics are tools that statisticians use to draw conclusions about the
characteristics of a population, drawn from the characteristics of a sample, and to decide how
certain they can be of the reliability of those conclusions.

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3.0 DATA

YEAR 2018 2019 2020

MONTHS (RM Million) (RM Million) (RM Million)

JANUARY 83,252.4 85,399.9 84,114.1
FEBRUARY 70,552.3 66,599.5 74,451.0
84,855.7 84,063.2 80,118.9
MARCH 84,636.4 85,155.0 64,786.6
APRIL 82,862.0 84,138.2 62,649.6
MAY 78,845.2 76,143.2 82,819.5
JUNE 86,474.6 87,958.4 92,559.0
JULY 81,982.2 81,357.4 79,129.8
AUGUST 83,341.9 77,721.3 88,905.4
SEPTEMBER 97,122.0 90,594.0 91,051.7
OCTOBER 85,542.5 80,872.3 84,661.0
NOVEMBER 84,119.5 86,400.3 95,741.3
DECEMBER

1. Number of class, k 2. Class width, c 3. Starting point = 62649.6

= 1 + 3.33
= 1 + 3.33 36 =
= 6.18
= 6 97122.0 − 62649.6
= 6
= 5745.4
= 5745

6

4.0 FREQUENCY TABLE Tally Frequency
III 3
Number of total I 1
exports (RM Million) IIII 5
18
62649.6 – 68393.6 IIII IIII IIII III 6
68394.6 – 74138.6 IIII I 3
74139.6 – 79883.6 III
79884.6 – 85628.6

85629.6 – 91373.6
91374.6 – 97118.6

Number of total Frequency Lower Upper Midpoint Cumulative
exports ( RM boundary boundary 65521.6 Frequency
Million)
68394.1 3
62649.6 – 68393.6 3 62649.1

68394.6 – 74138.6 1 68394.1 74139.1 71266.6 4

74139.6 – 79883.6 5 74139.1 79884.1 77011.6 9

79884.6 – 85628.6 18 79884.1 85629.1 82756.6 27

85629.6 – 91373.6 6 85629.1 91374.1 88501.6 33

91374.6 – 97118.6 3 91374.1 97119.1 94246.6 36

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5.0 CENTRAL TENDENCY AND DISPERSION

5.1 Mean

Number of total Frequency, Midpoint, fx
exports (RM Million) f x
196564.8
62649.6 – 68393.6 3 65521.6 71266.6
68394.6 – 74138.6 1 71266.6 385058
74139.6 – 79883.6 5 77011.6 1489618.8
79884.6 – 85628.6 18 82756.6 531009.6
85629.6 – 91373.6 6 88501.6 282739.8
91374.6 – 97118.6 3 94246.6

෍ = 36 ෍ = 2956257.6

Mean, = σ
σ

= 2956257.6

36

= 82118.27

8

5.2 Median, m

Number of total Frequency, Cumulative Lower boundary
exports (RM Million) f frequency,
62649.1
62649.6 – 68393.6 3 F 68394.1
68394.6 – 74138.6 1 3 74139.1
74139.6 – 79883.6 5 79884.1
79884.6 – 85628.6 18 4 85629.1
85629.6 – 91373.6 6 91374.1
91374.6 – 97118.6 3 9

27

33

36

Median class Median, m = + 2 −

Determine the class which median lies :
= 79884.1 + 36 −9 5745
36 2
2 + 1 = 2 + 1 = 19
18
Lm = 79884.1
N = 36 = 82756.6
F=9
fm = 18
C = 5745

9

5.3 Mode

Number of total Frequency, Cumulative Lower boundary
exports (RM Million) f frequency,
62649.1
62649.6 – 68393.6 3 F 68394.1
68394.6 – 74138.6 1 74139.1
74139.6 – 79883.6 5 3 79884.1
79884.6 – 85628.6 18 4 85629.1
85629.6 – 91373.6 6 9 91374.1
91374.6 – 97118.6 3 27
33
36

(Highest Frequency) Mode = + 1
1+ 2
L = 79884.1
d1 = 18-5 = 79884.1 + 13 5745
13+12
= 13
d2 = 18-6 = 82871.5

= 12
C = 5745

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5.4 Mean deviation, E

Number of total Frequency, Midpoint, fx − −
exports (RM f x
Million) 196564.8 16596.67 49790.01
3 65521.6 71266.6
62649.6 – 68393.6 385058
1489618.8
68394.6 – 74138.6 1 71266.6 531009.6 10851.67 10851.67
74139.6 – 79883.6 5 77011.6 282739.8
79884.6 – 85628.6 18 82756.6 5106.67 25533.35

638.33 11489.94

85629.6 – 91373.6 6 88501.6 6383.33 38299.98
91374.6 – 97118.6 3 94246.6 12128.33 36384.99

෍ = 36 ෍ = 2956257.6 ෍ −
=172349.94

Mean deviation, E = σ − f
σ

= 172349.94
36

= 4787.5

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5.5 Variance, and Standard Deviation,

Number of Frequency, Midpoint, − − −
total exports f x
16596.67 275449455.1 826348365.3
(RM 3 65521.6 10851.67 117758741.8 117758741.8
Million) 1 71266.6 5106.67 26078078.49 130390392.4
62649.6 – 5 77011.6 638.33 407465.19 7334373.4
68393.6 18 82756.6 6383.33 40746901.9 244481411.4
68394.6 – 6 88501.6 12128.33 147096388.6 441289165.8
74138.6 3 94246.6
74139.6 –
79883.6
79884.6 –
85628.6
85629.6 –
91373.6
91374.6 –
97118.6

෍ = 36 ෍ − 2
=1767602450

Variance, 2 Standard deviation, s

2 = σ − 2 =
σ = 49100068.06
= 7007.14
2 = 1767602450
36

2 = 49100068.06

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5.6 85th Percentile

Number of total Frequency, Cumulative Lower
exports (RM f frequency, boundary
Million)
3 F
62649.6 – 68393.6 1
68394.6 – 74138.6 5 3 62649.1
74139.6 – 79883.6 18 4 68394.1
79884.6 – 85628.6 6 9 74139.1
85629.6 – 91373.6 3 27 79884.1
91374.6 – 97118.6 33 85629.1
36 91374.1

Position of 85th percentile = 85 + −
85 × 36 100

85 = 100 = 100 = 30.6 85

85 = 85629.1 = 85629.1 + 85 ×36 − 27 5745
= 27 100
= 36
= 89076.1
85 = 6
= 5745

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6.0 HISTOGRAM AND OGIVE GRAPH

6.1 Histogram Graph
▪ Mode is determined from the histogram graph
▪ In histogram graph, the peak of data set or the tallest graph bar, where mid
point of its class is the Mode.

From the graph, Mode is 82871.5

Number of Frequency Lower boundary Upper Midpoint
Exports boundary 65521.6

62649.6 – 68393.6 3 62649.1 68394.1

68394.6 -74138.6 1 68394.1 74139.1 71266.6

74139.6 – 79883.6 5 74139.1 79884.1 77011.6

79884.6 – 85628.6 18 79884.1 85629.1 82756.6

85629.6 – 91373.6 6 85629.1 91374.1 88501.6

91374.6 – 97118.6 3 91374.1 97119.1 94246.6

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6.1.1 Mode Mode: 82871.5
85629.1 − 79884.1
10 = 574.5 per small box
= 79884.1 + (5 1 × 574.5)

5

82871.5

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6.2 Ogive Graph

▪ Median determined from ogive graph
▪ In ogive graph a new class was added with frequency 0
▪ Location on the y-axis 18

From the graph median is 82756.6

Number of exports Frequency Cumulative Upper boundary
frequency
56904.6 - 62648.6 0 62649.1
62649.6 – 68393.6 3 0 68394.1
68394.6 -74138.6 1 3 74139.1
74139.6 – 79883.6 5 4 79884.1
79884.6 – 85628.6 18 9 85629.1
85629.6 – 91373.6 6 27 91374.1
91374.6 – 97118.6 3 33 97119.1
36

16

82756.6

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7.0 MEASURE QUARTILE & DECILE USING FORMULA & GRAPH

Number of exports Frequency Cumulative Class boundaries
frequency
62649.6 – 68393.6 3 62649.1 – 68394.1
68394.6 -74138.6 1 3 68394.1 – 74139.1
74139.6 – 79883.6 5 4 74139.1 – 79884.1
79884.6 – 85628.6 18 9 79884.1 – 85629.1
85629.6 – 91373.6 6 27 85629.1 -91374.1
91374.6 – 97118.6 3 33 91374.1 – 97119.1
36

7.1 First Quartile

1= 1 + − 36 − 4 x 5745 = 79884.1
4 C = 74139.1 +
1 4

5

7.2 Third Quartile

3= 3 + 3 − C = 79884.1 + 3(36) − 9 x 5745 = 85629.1
4
4
3
18

7.3 Interquartile range

= Third quartile – First quartile
= 85629.1 – 79884.1
= 5745

18

7.1 First Quartile 7.2 Third Quartile

Location on the y-axis : 1 × 36 = 9 Location on the y-axis : 3 × 36 = 27
4 4

From the graph, the first quartile, 1 = 79884.1 From graph, the first quartile, 1 = 85629.1

19

7.4 Decile

3= + − 3 × 36 − 9 x 5745 = 80458.6
10 C = 79884.1 +
10
18

Location on the y-axis : 3 × 36 = 10.8
10

From the graph, the third decile, 3= 80458.6

20

8.0 DISCUSSION AND CONCLUSION

As a conclusion, according to the frequency table, the central tendency and
dispersion and also the graph, we can determine the Malaysian’s export for
every month from 2018 to 2020. The histogram graph that we construct
using all the data is a unimodal shaped graph. Then, we have constructed an
ogive graph too. The ogive graph’s first curve is in concave up shape. This
shows that the export was increasing at the beginning. Next, the curve is in
concave down shape which shows decrement in the export. This proves that
the Malaysian’s export for every month from 2018 to 2020 decreased.

There are lot of factors which influences the Malaysian’s export for every
month form 2018 to 2020. These factors include everything from political
circumstances, currency exchange rates, social and consumer behaviour,
factor endowments (labour, capital and land), productivity, to trade
policies, inflation and also demand. Other than that, the main reason of
export decrement is the covid-19 pandemic. During the pandemic season,
everything was affected especially economy of Malaysia which leads to
lack of export.

To improve and recover our Malaysia’s export for every month, we can
take some effort such as to examine our target countries’ growth rates,
internal market practices and pricing structures. Assess and re-assess our
competition and whether our product makes sense in the target market.
Importantly, price correctly for our export markets. When setting the price
for our product, we must make sure it reflects local market averages,
inflation rates, expectations, and currency conversions. Finally, we can
improve Malaysia’s export and maintain it consistently.

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9.0 REFERENCES

Azhar, S. (2020/2021, October 6). StuDocu. Retrieved from StuDocu.com:
https://www.studocu.com/my/document/politeknik-sultan-haji-ahmad-shah/mechanical-
engineering/case-study-math-reportdraft/14204570

DukeMoon1427. (n.d.). CASE STUDY DBM30033 ENGINEEERING MATHEMATICS 3.
Retrieved from coursehero.com:
https://www.coursehero.com/file/71106151/CASE-STUDYdocx/

MALAYSIA EXTERNAL TRADE STATISTICS. (2019). Retrieved from miti.gov.my:
https://www.miti.gov.my/miti/resources/Media%20Release/Malaysia_External_Trade_
Statistics_-_Trade_Performance_For_2019_And_December_2019.pdf

MALAYSIA EXTERNAL TRADE STATISTICS. (2021, January 30). Retrieved from miti.gov.my:
https://www.miti.gov.my/miti/resources/Media%20Release/Trade_Performance_for_
the_Month_of_November_2018_and_the_Period_of_January_-_November_2018.pdf

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