Question

Find the value of p, when the mean of the following distribution is 20.
$\begin{array}{cccccc}\text{x}& 15& 17& 19& 20+p& 23\\ \text{f}& 2& 3& 4& 5p& 6\end{array}$

Answer 1

We know that,
Mean = $\frac{\sum xifi}{\sum fi}$

Mean = $\frac{(15\times 2+17\times 3+19\times 4+(20+p)\times 5p+23\times 6)}{2+3+4+5p+6}$
⇒$20=\frac{(30+51+76+100p+5p^2+138)}{(15+5p)}$

⇒$5p^2=5$

⇒$p^2=55$
⇒$p^2=1$

⇒p=±1
Hence, the value of p is ±1.