Question

If the mean of the following data is 15, find p.

x:	5	10	15	20	25
f:	6	p	6	10	5

Answer 1

Calculation of Mean

xi	fi	fi xi
5	6	30
10	p	10p
15	6	90
20	10	200
25	5	125
Total	${\sum }_{}{f}_i$ = 27 + p	${\sum }_{}{f}_i{x}_i$ = 445 + 10p

We have:

${\sum }_{}{f}_i$ = 27 + p, ​${\sum }_{}{f}_i{x}_i$ = 445 +10p

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

$$\begin{gathered} \Rightarrow 15=\frac{445+10p}{27+p} \\ \Rightarrow 15(27+p)=445+10p\Rightarrow 405+15p=445+10p\Rightarrow 15p-10p=445-405\Rightarrow 5p=40\Rightarrow p=40÷5 \end{gathered}$$

Therefore, p = 8.