Question

The mean of following frequency distribution is 54. Find the value of p.

Class	0-20	20-40	40-60	60-80	80-100
Frequency	7	p	10	9	13

 

Answer 1

The given data is shown as follows:

Class	Frequency`(f_i)`	Class mark `(x_i)`	`f_i  x_i`
0-20	7	10	70
20-40	p	30	30p
40-60	10	50	500
60-80	9	70	630
80-100	13	90	1170
Total	`sum f_i=39+p`		`sum f_i x_i = 2370 + 30p`

The mean of the given data is given by,
x =`(sum_(i) f_i x_i)/(sum _(i)f_i)`
⇒ 54 =`(2370+30p)/(39+p)`
⇒ 54 (39 + p) = 2370 + 30p
⇒ 2106 + 54p = 2370 – 2106
⇒ 24p = 264
⇒ p = 11
Hence, the value of p is 11.