Question

Find the value of p for the following frequency distribution whose mean is 16.6

x	8	12	15	p	20	25	30
f	12	16	20	24	16	8	4

Answer 1

We will make the following table:

(xi)	(fi)	(fi)(xi)
8	12	96
12	16	192
15	20	300
p	24	24p
20	16	320
25	8	200
30	4	120
	$\sum _{}^{}{f}_i=$100	$\sum _{}^{}{f}_i{x}_i=$1228 + 24p

Thus, we have:

$\mathrm{Mean}=\frac{{\displaystyle \underset{}{\overset{}{\sum f_i{x}_i}}}}{{\displaystyle \sum _{}^{}}{x}_i}$
$$\begin{gathered} \Rightarrow 16.6=\frac{\left(1228+24p\right)}{100} \\ \Rightarrow 16.6\times 100=\left(1228+24p\right) \\ \Rightarrow 1660=1228+24p \end{gathered}$$
$$\begin{gathered} \Rightarrow 24p=432 \\ \Rightarrow p=18 \end{gathered}$$