Question

The mean of the following frequency distribution is 25.8 and the sum of all the frequencies is 50. Find x and y. 

Class	0-10	10-20	20-30	30-40	40-50
Frequency	7	x	15	y	10

Answer 1

Class Interval	xi	fi	fixi
0-10	5	7	35
10-20	15	x	15x
20-30	25	15	375
30-40	35	y	35y
40-50	45	10	450
Total		50	860 + 15x + 35y

`Σf_i = x_1 + x_2 + ..... + x_n`

50 = 7 + x + 15 + y + 10 

⇒ x + y + 32 = 50

⇒ x + y = 18 ........... (i) 

`barx = (Σf_ix_i)/(Σf)`

`25.8 = (860 + 15x + 35y )/50` 

⇒  15x + 35y + 860 = 1290 

⇒ 15x + 35y = 430 

⇒ 3x + 7y = 86 ............. (ii) 

Multiplying (i) by 3 and subtracting from (ii) 

4y = 32 

⇒ y = 8 

Putting value of y in (i) 

x + 8 = 18 
x = 10 

Therefore, x = 10 and y = 8