VARIANCE FOR GROUPED AND UNGROUPED DATA

Question 1 :

Calculate the variance of the following table.

x    2    4    6     8    10    12    14    16

f    4    4    5    15     8      5      4    5

Solution :

x

2

4

6

8

10

12

14

16

f

4

4

5

15

8

5

4

5

d = x-8

2-8 = -6

4-8 = -4

6-8 = -2

8-8 = 0

10-8 = 2

12-8 = 4

14-8 = 6

16-8 = 8

d2

36

16

4

0

4

16

36

64

fd2

144

64

20

0

32

80

144

320

Σf  =  50 and Σfd²  =  804

σ2  =  √(Σfd²/Σf)

=  √(804/50)

=  16.08

Question 2 :

Find the variance of the following distribution

Class interval

20-24

25-29

30-34

35-39

40-44

45-49

Frequency

15

25

28

12

12

8

Solution :

Here we consider the first data that is class interval as (x) and no of frequency as (f).

x

22

27

32

37

42

47

f

15

25

28

12

12

8

d = x-32

22-32 = -10

27-32 = -5

32-32 = 0

37-32 = 5

42-32 = 10

47-32 = 15

d2

100

25

0

25

100

225

fd2

1500

625

0

300

1200

1800

Σfd² =  5425 and Σf  =  100

 σ  =  √(Σfd²/Σf)

=  √(5425/100)

=  √54.25

=   7.37

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