Find the mean and variance for the following frequency distribution.

Classes

0-10

10-20

20-30

30-40

40-50

Frequencies

5

8

15

16

6

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Solution

Class

Frequency

f_i

Mid-point x_i

y_i²

f_iy_i

f_iy_i²

0-10

5

5

–2

4

–10

20

10-20

8

15

–1

1

–8

8

20-30

15

25

0

0

0

0

30-40

16

35

1

1

16

16

40-50

6

45

2

4

12

24

50

10

68

Mean,

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