Question

If the mean of the following distribution is 54, find the value of p.

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

Answer 1

Class interval	`bb(f_i)`	`bb(x_i)` (Mid-value)	`bb(d_i = (x_i - 30)/h)`	`bb(f_i d_i)`
0 – 20	7	10	–1	–7
20 – 40	p	30	0	0
40 – 60	10	50	1	10
60 – 80	9	70	2	18
80 – 100	13	90	3	39
Total	39 + p			60

Assumed mean (A) = 30

Width of the interval (h) = 20

Mean = 54

Mean = `A + ((sum f_i d_i)/f_i) h`

54 = `30 + (60/(39 + p)) xx 20`

`54 - 30 = 60/(39 + p) xx 20`

24 = `1200/(39 + p)`

39 + p = `1200/24`

39 + p = 50

p = 50 − 39

⇒ p = 11