Find the value of 'p' if the mean of the following data is 17. xi10

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Find the value of 'p' if the mean of the following data is 17.
$\begin{matrix} x_{i} & 10 & p & 18 & 21 & 25 f_{i} & 10 & 15 & 7 & 9 & 9 \end{matrix}$

Options:

A . 12

B . 14

C . 16

D . 18

Answer: Option B
:
B

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

$\begin{matrix} x_{i} & 10 & p & 18 & 21 & 25 f_{i} & 10 & 15 & 7 & 9 & 9 x_{i} f_{i} & 100 & 15 p & 126 & 189 & 225 \end{matrix}$
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

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