Vedanta Excel in Opt. Mathematics Book 7 Final (2078)

Statistics

(a) Mode for Individual Series
In case of individual series, mode can be found by inspection. To find the
mode, count the number of times the various values repeat themselves. Then,
the maximum number of repeated value (i.e., value with maximum frequency)
is the mode. Here, we study mode for individual and discrete series.

Worked Out Examples

Example 1. Find the mode from the following data.
Solution: 15, 10, 14, 15, 18, 20, 15, 14, 13, 10, 15, 18
Calculation of mode

Variate value No. of occurrence (Frequency)
10 2
13 1
14 2
15 4
18 2
20 1

From above table the value 15 is 4 times repeated. 4 is the
maximum frequency whose corresponding value is 15.

? Mode (MO) = 15

(b) Mode for Discrete Series

In this series, mode can be found simply by inspection. The value with the
maximum frequency is the mode.

Example 2. Find the mode from the given table:

Marks 40 50 60 70 80 90 100

No. of students 4 6 12 16 12 4 2

Solution: Here, the maximum frequency is 16 whose corresponding value is 70.

? Mode (MO) = 70

Exercise 7.4

Short Questions :
1. Find the modal value of the following data:

(a) 7, 8, 10, 7, 10, 7, 8, 7, 12, 7, 13, 7, 8

vedanta Excel in Additional Mathematics - Book 7 121

Statistics

(b) 2, 4, 6, 8, 6, 8, 7, 8, 8, 10, 12, 6
(c) 100, 200, 300, 300, 400, 500, 300, 100, 400, 500, 300
2. Find the modal value of the following data :

(a) Age (years) 10 12 16 18 20 22
No. of people 4 6 12 8 4 3

(b) x 20 30 40 50 60 70 80
f 2 6 10 15 12 13 6

(c) Size of shoes 3 4 5 6 7 8 9 10
No. of persons 10 15 20 12 8 6 4 2

Long Questions :
3. (a) A boy scored the following marks in 11 tests of different units:

10, 12, 15, 16, 12, 13, 15, 14, 15, 18, 15
(i) What is the modal marks of the boy?
(ii) What is his median marks?
(iii) What is his mean marks?
(b) A Selesman sold the shoes of the following sizes.
2, 4, 6, 4, 6, 8, 4, 6, 8, 7, 6, 2, 5, 8, 6
(i) What is the model size of the shoes?
(ii) Find the median size of the shoes.
(iii) Find the mean size of the shoes.

1. (a) 7 (b) 8 (c) 300
2. (a) 16 (b) 50 (c) 5
3. (a) (i) MO = 15 (ii) Md = 15 (iii) X = 14.09
(ii) Md = 6 (iii) X = 5.47
(b) (i) MO = 6

122 vedanta Excel in Additional Mathematics - Book 7

Statistics

Model Questions

Class : 7 Annual Examination Full marks : 50
Time : 1.5 hours

Attempt all the questions.

Group A [9×2 = 18]

1. Find the values of x and y of x , y = (2, 3).
3 4

2. If A = 1 2 and B = 2 –4 , find (A + B).
4 5 6 2

3. Find the distance between P(6, 7) and Q(–2, 1).

4. Simplify : 32 – 8 + 12 2

5. State Pythagoras theorem with figure.

6. Prove that (1 – sin2A) (1 + cot2A) = cot2A

7. Find the images of P(7, 8) and Q(2, 3) when they are reflected on X-axis.

8. Find the arithmetic mean of given data :

10, 20, 30, 40, 50, 60, 70

9. Find the mode of given data :

6, 8, 12, 8, 12, 14, 16, 18, 12, 15, 12

Group B [8×4 = 32]

10. If R = {(1, 1), (2, 4), (3, 9), (4, 16)} is a relation, show it in the following ways.

(a) Table method 123
(b) Arrow diagram method
(c) Graphical method
(d) Rule method

vedanta Excel in Additional Mathematics - Book 7