Question

If the mean of the following data is $20.2$, find the value of $\mathrm{p}$:

$\mathrm{x}$	$10$	$15$	$20$	$25$	$30$
$\mathrm{f}$	$6$	$8$	$\mathrm{p}$	$10$	$6$

Answer 1

Find the required value:

The formula of mean: $\mathrm{Mean}=\frac{{\displaystyle \sum _{\mathrm{i}}{\mathrm{f}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}}}{{\displaystyle \underset{\mathrm{i}}{\sum {\mathrm{f}}_{\mathrm{i}}}}}$

Given Mean $=20.2$

$$\begin{gathered} \Rightarrow \mathrm{Mean}=\frac{(10\times 6)+(15\times 8)+(20\times \mathrm{p})+(25\times 10)+(30\times 6)}{6+8+\mathrm{p}+10+6} \\ \Rightarrow 20.2=\frac{610+20\mathrm{p}}{30+\mathrm{p}} \\ \Rightarrow 20.2(30+\mathrm{p})=610+20\mathrm{p} \\ \Rightarrow 606+20.2\mathrm{p}=610+20\mathrm{p} \\ \Rightarrow 20.2\mathrm{p}-20\mathrm{p}=610-606 \\ \Rightarrow 0.2\mathrm{p}=4 \\ \Rightarrow \mathrm{p}=\frac{4}{0.2} \\ \Rightarrow \mathrm{p}=20 \end{gathered}$$

Hence, the value of $\mathrm{p}$ is $20$.