Question

The mean of the following data is 20.6. Find the value of p.

x:	10	15	p	25	35
f:	3	10	25	7	5

Answer 1

Calculation of Mean

xi	fi	fi xi
10	3	30
15	10	150
p	25	25p
25	7	175
35	5	175
Total	${\sum }_{}{f}_i$ = 50	${\sum }_{}{f}_i{x}_i$ = 530 + 25p

We have:

${\sum }_{}{f}_i$ = 50, ​${\sum }_{}{f}_i{x}_i$ = 530 +25p

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

$$\begin{gathered} \Rightarrow 20.6=\frac{530+25p}{50} \\ \Rightarrow 20.6\times 50=530+25p\Rightarrow 1030=530+25p\Rightarrow 1030-530=25p\Rightarrow 500=25p\Rightarrow p=\frac{500}{25}\Rightarrow p=20 \end{gathered}$$