If the mean of the following frequency distribution table is 24, let us find the value of p.

Given that, mean = 24

We need to find the value of p.

To find p, we need to calculate mean by direct method.

Let us make a table showing frequencies, midpoints and f_ix_i.

We have

∑f_ix_i = 1700 + 35p

∑f_i = 80 + p

By direct method, we have the formula of arithmetic mean:

⇒

⇒ 24 × (80 + p) = 1700 + 35p

⇒ 1920 + 24p = 1700 + 35p

⇒ 35p – 24p = 1920 – 1700

⇒ 11p = 220

⇒

⇒ p = 20

Thus, p = 20.