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

p = 0

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p = 1

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p = 2

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Data insufficient

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Solution

The correct option is A $p = 1$
$x$ $f$ $f x$
$15$ $2$ $30$
$17$ $3$ $51$
$19$ $4$ $76$
$(20 + p)$
$5 p$ $100 p + 5 p^{2}$
$23$ $6$ $138$

$\sum f = 15 + 5 p$

$\sum f x = 295 + 100 p + 5 p^{2}$

Mean $¯ ¯ ¯ x = \frac{\sum f x}{\sum f} = \frac{295 + 100 p + 5 p^{2}}{15 + 5 p}$
$\Rightarrow 20 = \frac{295 + 100 p + 5 p^{2}}{15 + 5 p}$
$\Rightarrow 300 + 100 p = 295 + 100 p + 5 p^{2}$
$\Rightarrow 5 p^{2} = 5$

$\Rightarrow p = 1$ or $- 1$

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Similar questions

p

20

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

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

p

18

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

p

7.5

$x$	$3$	$5$	$7$	$9$	$11$	$13$
$f$	$6$	$8$	$15$	$p$	$8$	$4$

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

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