Find the value of $p$ , if the mean of the following distribution is $20$ .
$x$ : $15$ $17$ $19$ $20 + p$ $23$
$f$ : $2$ $3$ $4$ $5 p$ $6$

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Solution

The correct option is A $1$
Mean = $\frac{\sum x_{i} f_{i}}{\sum f_{i}}$

$\Rightarrow$ mean = $\frac{(15 \times 2) + (17 \times 3) + (19 \times 4) + ((20 + p) \times 5 p) + (23 \times 6)}{2 + 3 + 4 + 5 p + 6}$

$\Rightarrow$ mean = $\frac{30 + 51 + 76 + (20 + p) (5 p) + 138}{2 + 3 + 4 + 5 p + 6} = 20$

$\Rightarrow 295 + 100 p + 5 p^{2} = 300 + 100 p$

$\Rightarrow 5 p^{2} = 5$

$\Rightarrow p = 1$

Suggest Corrections

Variate $(x)$	$13$	$15$	$17$	$19$	$20 + p$	$23$
Frequency $(f)$	$8$	$2$	$3$	$4$	$5 p$	$6$

x:	15	17	19	20+p	23
f:	2	3	4	5p	6

x:	15	17	19	20+p	23
f:	2	3	4	5p	6