Question

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

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

Answer 1

​ Calculation of Mean

xi	fi	fixi
8	12	96
12	16	192
15	20	300
p	24	24p
20	16	320
25	8	200
30	4	120
Total	$\sum _{}{f}_i$= N = 100	$\sum _{}{f}_i{x_i}_{}$ = 1228 + 24p

We have:

$\sum _{}{f}_i$ = 100, $\sum _{}{f}_i{x_i}_{}$ = 1228 +24p

∴ Mean $=\frac{\sum _{}{f}_i{x}_i}{\sum _{}{f}_i}$

$$\begin{gathered} \Rightarrow 16.6=\frac{1228+24p}{100} \\ \Rightarrow 16.6\times 100=1228+24p \\ \Rightarrow 1660=1228+24p \\ \Rightarrow 1660-1228=24p \\ \Rightarrow 432=24p \\ \Rightarrow p=\frac{432}{24} \\ \Rightarrow p=18. \end{gathered}$$