If the mean of the following distribution is 6, find the value of p.
x: $2$ $4$ $6$ $10$ $p + 5$
f: $3$ $2$ $3$ $1$ $2$

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Solution

$x_{i}$

$f_{i}$

$f_{i} x_{i}$
$2$ $3$ $6$
$4$ $2$ $8$
$6$ $3$ $18$
$10$ $1$ $10$

$N = \sum f_{i} = 11$ $\sum f_{i} x_{i} = 2 (p + 5)$

We have, $N = \sum f_{i} = 11, \sum f_{i} x_{i} = 2 p + 52$
$∴$ Mean = $\frac{\sum f_{i} x_{i}}{N} = 6 \frac{2 p + 52}{11} \Rightarrow 66 = 2 p + 52 \Rightarrow 2 p = 14 \Rightarrow p = 7$

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x : 24610 p + 5

f : 32312

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

If the mean of the following distribution is 6, find the value of 'P'.

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k

$x$	$2$	$4$	$6$	$8$	$10$
$f$	$5$	$3$	$7$	$6$	$k$

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