Question

Find the values of x and y if the mean and total frequency of the distribution are 25 and 50 respectively.

Class Interval	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Frequency	7	x	5	y	4	2

Answer 1

Given: Mean = 25

Class Interval	Frequency `(f_i)`	Class mark `(x_i)`	`d_i = x_i - 25`	`f_i d_i`
0 – 10	7	5	– 20	– 140
10 – 20	x	15	– 10	– 10x
20 – 30	5	25 = A	0	0
30 – 40	y	35	10	10y
40 – 50	4	45	20	80
50 – 60	2	55	30	60
	`sumf_i = 18 + x + y`			`sumf_i d_i = 10y - 10x`

Mean = 25   .......[Given]

Also, Mean, `bar"X" = "A" + (sumf_i d_i)/(sumf_i)`

25 = `25 + (10y - 10x)/(18 + x + y)`

25 – 25 = `(10y - 10x)/(18 + x + y)`

0 = `(10y - 10x)/(18 + x + y)`

0 (18 + x + y) = 10y – 10x

10y – 10x = 0

y – x = 0  ......(i)

Also, 50 = 18 + x + y

x + y = 50 – 18

x + y = 32  ......(ii)

Adding equations (i) and (ii), we get

2y = 32

y = 16

Putting the value of y in equation (ii), we get

x + 16 = 32

x = 32 – 16 = 16

As a result, x and y have values of 16 and 16, respectively.