Question

The mean of the following frequency distribution is 8. Find the value of p.

x	3	5	7	9	11	13
f	6	8	15	p	8	4

Answer 1

(xi)	(fi)	(fi)(xi)
3	6	18
5	8	40
7	15	105
9	p	9p
11	8	88
13	4	52
	$\sum _{}^{}{f}_i$ = 41 + p	$\sum _{}^{}{f}_i{x}_i=$303 + 9p

We have:

$\mathrm{Mean}=\frac{{\displaystyle \sum _{}^{}}{x}_i{f}_i}{{\displaystyle \sum _{}^{}}{f}_i}$

$$\begin{gathered} \Rightarrow 8=\frac{303+9p}{41+p} \\ \Rightarrow 328+8p=303+9p \\ \Rightarrow 25=p \end{gathered}$$