If the mean of the following distribution is $10$ , find the value of $m$ .
$X$
$12$
$4$
$6 + m$
$8$
$10$
$F$
$10$
$15$
$25$
$24$
$16$

7.72

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8.72

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6.72

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9.72

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Solution

The correct option is B $8.72$
$X_{i}$ $F_{i}$ $X_{i} F_{i}$
12 10 12 x 10 = 120
4 15 4 x 15 =60
6+m 25 150+25 m
8 24 8 x 24 = 192
10 16 10 x 16 =160
$Σ F_{i} = 90$ $Σ X_{i} F_{i} = 682 + 25 m$

Mean $=$ $\frac{\sum X_{i} F_{i}}{\sum F_{i}}$
$10 = \frac{682 + 25 m}{90}$
$900 - 682 = 25$ $m$
$218 = 25$ $m$
$m = 8.72$

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Similar questions

If the mean of the following frequency distribution is $7.2$ find value of $k$ .

$\begin{matrix} x & 2 & 4 & 6 & 8 & 10 & 12 f & 4 & 7 & 10 & 16 & k & 3 \end{matrix}$

p

16.6

$x$ :	$8$	$12$	$15$	$p$	$20$	$25$	$30$
$f$ :	$12$	$16$	$20$	$24$	$16$	$8$	$4$

8

^{'} k^{'}

$x$	$2$	$4$	$6$	$8$	$10$	$12$
$f r e q u e n c y = f$	$4$	$7$	$10$	$16$	$k$	$3$

x:	8	12	15	p	20	25	30
f:	12	16	20	24	16	8	4

Locate median of the following distribution :

$\begin{matrix} Variable (X) & 10 & 11 & 12 & 13 & 14 & 15 & 16 Frequency (f) & 8 & 15 & 25 & 20 & 12 & 10 & 5 \end{matrix}$

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