Question

If the average of the following data is 20.2, find the value of p:
$\begin{array}{cc}x& f\\ 10& 6\\ 15& 8\\ 20& P\\ 25& 10\\ 30& 6\end{array}$

• A. 10
• B. 16
• C. 20
• D. 14

Answer 1

The correct option is C 20

$$\begin{array}{ccc}\left(x_i\right)& f_i& f_i{x}_i\\ \text{10}& \text{6}& \text{60}\\ \text{15}& \text{8}& \text{120}\\ \text{20}& \text{P}& \text{20P}\\ \text{25}& \text{10}& \text{250}\\ \text{30}& \text{6}& \text{180}\\ & \sum f_i=30+P& \sum f_i{x}_i=610+20P\end{array}$$
Given that Mean = 20.2
$\because Mean=\frac{\sum f_i{x}_i}{\sum f_i}\Rightarrow 20.2=\frac{610+20P}{30+P}$

$\Rightarrow$ 20.2 ( 30 + P ) = 610 + 20P
$\Rightarrow$ 606 + 20.2P = 610 + 20P
$\Rightarrow$ 20.2P – 20P = 610 – 606
$\Rightarrow$ 0.2 P = 4
$\Rightarrow$ P = 20
$\therefore$ The value of 'P' is 20.