Question

Calculate mean, median and mode from the

following frequency distribution.

Variable: 10-13 13-16 16-19 19-22 22-25 25-28

Frequency: 8 15 27 51 75 54

Variable: 28-31 31-34 34-37 37-40

Frequency: 36 18 9 7​

Answer 1

Answer:

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Answer 2

Given :

Variable: 10-13 13-16 16-19 19-22 22-25 25-28 28-31 31-34 34-37 37-40

Frequency: 8      15      27     51      75        54       36        18       9     7​

To Find : mean, median and mode

 

Solution:

CI                 f           cf

10 - 13          8         8

13  - 16        15        23

16  - 19        27       50

19  - 22        51        101

22  - 25       75        176

25  -28        54       230

28  - 31        36       266

31  - 34        18        284

34  - 37        9        291

37  -  40       7        300

Mode lies in  22  - 25   as max f = 75

Mode = 22  +  3 * ( 75 - 51) / (75 - 51 + 75 - 54)

= 22 + 3 *  24 / (45)

= 22 + 1.6

= 23.6

Median also lies in 22-25         (300/2 = 150)

Median = 22 + 3 * ( 150 - 101)/75

= 22 + 1.96

= 23.96

11.5         8 92

14.5        15 217.5

17.5        27 472.5

20.5 51 1045.5

23.5 75 1762.5

26.5 54 1431

29.5 36 1062

32.5 18 585

35.5 9 319.5

38.5 7 269.5

    300 7257

Mean =  7257/300  = 24.19

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