Question

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

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

Answer 1

The given data is shown as follows:

Class	Frequency (fi)	Class mark (xi)	fixi
0−20	7	10	70
20−40	p	30	30p
40−60	10	50	500
60−80	9	70	630
80−100	13	90	1170
Total	∑ fi = 39 + p		∑ fixi = 2370 + 30p

The mean of given data is given by

$$\begin{gathered} \overline{x}=\frac{{\displaystyle \sum _i}{f}_i{x}_i}{{\displaystyle \sum _i}{f}_i} \\ \Rightarrow 54=\frac{2370+30p}{39+p} \\ \Rightarrow 54(39+p)=2370+30p \\ \Rightarrow 2106+54p=2370+30p \\ \Rightarrow 54p-30p=2370-2106 \\ \Rightarrow 24p=264 \\ \Rightarrow p=11 \end{gathered}$$

​Thus, the value of p is 11.