If the mean of the following frequency distribution is 54, find the value of p. [CBSE 2006]

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

For equal class intervals, we will solve by finding mid points of these classes using direct method.

We have got

Σf_i = 39 + p and Σf_ix_i = 2370 + 30p

∵ mean is given by

⇒ (∵ given: mean of pocket allowance is 54)

⇒ 2106 + 54p = 2370 + 30p

⇒ 54p – 30p = 2370 – 2106

⇒ 24p = 264

⇒ p = 11

Thus, p is 11.