Question

If the mean of the following frequency distibution is 24, find the value of p.
$\begin{array}{cccccc}\text{Class}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}& 3& 4& p& 3& 2\end{array}$

Answer 1

The given data is shown as follows:

Class	Frequency ($f_i$)	Class mark ($x_i$)	($f_i{x}_i$)
0 - 10	3	5	15
10 - 20	4	15	60
20 - 30	p	25	25p
30 - 40	3	35	105
40 - 50	2	45	90
Total	$\sum f_i$=12+p		$\sum f_i{x}_i$=270+25p

The mean of given data is given by

$\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}$

⇒ 24 = $\frac{270+25p}{12+p}$
⇒ 24(12 + p) = 270 + 25p
⇒288 + 24p = 270 + 25p
⇒ 25p - 24p = 288 - 270
⇒ p = 18

Hence, the value of p is 18.