Question

If the mean of the following distribution is 27, find the value of p.

Class	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50
Frequency	8	p	12	13	10

Answer 1

Class interval	Mid value(x1)	Frequency(f1)	f1x1
0 - 10	5	8	40
10 - 20	15	p	15p
20 - 30	25	12	300
30 - 40	35	13	455
40 - 50	45	10	450
		N = 43 + p	`sumf_1x_1=1245 + 15p`

Given

Mean = 27

`rArr(sumf_1x_1)/N=27`

`rArr(1245 + 15p)/(43+p)=27`

1245 + 15p = 27(43 + p)

1245 + 15p = 27p + 1161

27p - 15p = 1245 - 1161

12p = 84

p = 84/12 = 7