Question

If the mean of the following frequency distribution is 25, find the value of x and y.

CLASS : 18-20 20-22 22-24 24-26 26-28 28-30 30-32 TOTAL
FREQUENCY : 13 15 x 18 16 y 13 106

Answer 1

Given : mean of the following frequency distribution is 25,

CLASS : 18-20 20-22 22-24 24-26 26-28 28-30 30-32

FREQUENCY : 13 15 x 18 16 y 13 106​

To Find : Value of x and y

Solution:

CLASS : Mean class  A= (mean class - 25)/2   f        AF

18-20          19                    -3                            13        -39  

20-22         21                    -2                            15        -30

22-24          23                    -1                           x          -x

24-26          25                   0                            18         0

26-28          27                    1                            16         16

28-30          29                    2                           y         2y

30-32         31                     3                            13        39

                                                                   75+x + y     2y -x - 14

Assumed mean and mean are same

Hence 2y -x - 14 = 0

=> 2y - x = 14

75+x + y = 106

=>> x + y  = 31

=> 3y = 45

=> y = 15

x = 16

value of x and y.  

x = 16

y = 15

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