Question

If the mean of the following data is 20.2, find the value of p.
$\begin{array}{cccccc}\text{Variable}\left(x_i\right)& 10& 15& 20& 25& 30\\ \text{Frequency}\left(f_i\right)& 6& 8& p& 10& 6\end{array}$

Answer 1

Mean = $\frac{10\times 6+15\times 8+20\times p+25\times 10+30\times 6}{6+8+p+10+6}$
⇒$20.2=\frac{60+120+20p+250+180}{(30+p)}$
⇒$20.230+p=610+20p$
⇒$606+20.2p=610+20p$
⇒$20.2p-20p=610-606$

⇒$0.2p=4$
⇒$p=\frac{4}{0.2}$

⇒$p=\frac{40}{2}$

⇒$p=20$
Hence, the value of p is 20.