Question

If the mean of the following frequency distribution is 24, find the value of p. [CBSE 2013]

Class	0−10	10−20	20−30	30−40	40−50
Frequency	3	4	p	3	2

Answer 1

The given data is shown as follows:

Class	Frequency (fi)	Class mark (xi)	fixi
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	∑ fi = 12 + p		∑ fixi = 270 + 25p

The mean of given data is given by

$$\begin{gathered} \overline{x}=\frac{{\displaystyle \sum _i}{f}_i{x}_i}{{\displaystyle \sum _i}{f}_i} \\ \Rightarrow 24=\frac{270+25p}{12+p} \\ \Rightarrow 24(12+p)=270+25p \\ \Rightarrow 288+24p=270+25p \\ \Rightarrow 25p-24p=288-270 \\ \Rightarrow p=18 \end{gathered}$$

Hence, the value of p is 18.