Question

If the mean of the following data is 20.2, find the value of p.

Variable (xi)	10	15	20	25	30
Frequency (fi)	6	8	p	10	6

Answer 1

We know that,
Mean = $\frac{{\displaystyle \sum _{}{x}_i{f}_i}}{\sum _{}{f}_i}$

For the following data:

Variable (xi)	10	15	20	25	30
Frequency (fi)	6	8	p	10	6

Mean = $\frac{\left(10\times 6\right)+\left(15\times 8\right)+\left(20\times p\right)+\left(25\times 10\right)+\left(30\times 6\right)}{6+8+p+10+6}$
$$\begin{gathered} \Rightarrow 20.2=\frac{60+120+20p+250+180}{30+p} \\ \Rightarrow 20.2\left(30+p\right)=610+20p \\ \Rightarrow 606+20.2p=610+20p \\ \Rightarrow 20.2p-20p=610-606 \\ \Rightarrow 0.2p=4 \\ \Rightarrow p=\frac{4}{0.2} \\ \Rightarrow p=\frac{40}{2} \\ \Rightarrow p=20 \end{gathered}$$

Hence, the value of p is 20.