Question

Find the value of 'p' if the mean of the following data is 17.

$$\begin{array}{cccccc}{x}_i& 10& p& 18& 21& 25\\ f_i& 10& 15& 7& 9& 9\end{array}$$

• A. 12
• B. 14
• C. 16
• D. 18

Answer 1

The correct option is B

14

Average or mean value of a given number of observations is the sum of all the observations divided by the total number of observations.

$$\begin{array}{cccccc}{x}_i& 10& p& 18& 21& 25\\ f_i& 10& 15& 7& 9& 9\\ x_i{f}_i& 100& 15p& 126& 189& 225\end{array}$$
Mean $=\frac{\sum x_i{f}_i}{\sum f_i}$
$\sum x_i$$f_i$ = 100 + 15p + 126 + 189 + 225
= 640 + 15p

$\sum f_i$ = 50

given that mean = 17

$\Rightarrow$ 640 + 15p = 50 x 17
$\Rightarrow$ 15p = 210
$\Rightarrow$ p = 14