Question

If the mean of the following distribution is 27, find the value of p.

Class	0−10	10−20	20−30	30−40	40−50
Frequency	8	p	12	13	10

Answer 1

The given data is shown as follows:

Class	Frequency (fi)	Class mark (xi)	fixi
0−10	8	5	40
10−20	p	15	15p
20−30	12	25	300
30−40	13	35	455
40−50	10	45	450
Total	∑ fi = 43 + p		∑ fixi = 1245 + 15p

The mean of given data is given by

$$\begin{gathered} \overline{x}=\frac{{\displaystyle \sum _i}{f}_i{x}_i}{{\displaystyle \sum _i}{f}_i} \\ \Rightarrow 27=\frac{1245+15p}{43+p} \\ \Rightarrow 1161+27p=1245+15p \\ \Rightarrow 27p-15p=1245-1161 \\ \Rightarrow 12p=84 \\ \Rightarrow p=7 \end{gathered}$$

Thus, the value of p is 7.