Question

The mean of the following distribution is 53. Find the missing frequency p :

Class	0-20	20-40	40-60	60-80	80-100
Frequency	12	15	32	p	13

Answer 1

Class	Mid-Values(xi)	Frequency (fi)	fixi
0−20	10	12	120
20−40	30	15	450
40−60	50	32	1600
60−80	70	p	70p
80−100	90	13	1170
		∑fi = 72 + p	∑fixi = 3340 + 70p

Given,

Mean of the given frequency distribution = 53

Now, Mean = \(\frac{\sum f_i x_i}{\sum f_i}\)

⇒ 53 = \(\frac{3340 + 70p}{72 +p}\)

⇒ 53(72 + p) = 3340 + 70p

⇒ 53p − 70p = 3340 − 3816

⇒ 476 = 17p

⇒ p = 28

Thus, the value of p is 28.

Answer 2

or, 17p = 476

therefore, p = 476/17 = 28