The mean of the following distribution is $22,$ find the missing frequency $f$ :

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Solution

Class Frequency $(x_{i})$ $(f_{i})$ $(f_{i} x_{i})$
0-10
10-20
20-30
30-40
40-50 12
16
6
f
9
__
43+f 5
15
25
35
45 60
240
150
35 f
405
_
855+35 f
Mean = $\frac{\sum f_{i} x_{i}}{\sum x_{i}} = \frac{855 + 35 f}{(43 + f)}$
$\Rightarrow 22 = \frac{855 + 35 f}{(43 + f)}$
$\Rightarrow 996 + 22 f = 855 + 35 f$
$\Rightarrow 91 = 13 f$
$\Rightarrow f = 7$
$∴$ missing frequency is 7

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Similar questions

50

$x$ :	$10$	$30$	$50$	$70$	$90$
$f$ :	$17$	$f_{1}$	$32$	$f_{2}$	$19$	Total: $120$

50

150

$x$	$10$	$30$	$50$	$70$	$90$	$T o t a l$
$f$	$17$	$f_{1}$	$32$	$f_{2}$	$19$	$120$

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

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is $50$ .

$\begin{matrix} x_{i} & f_{i} 10 & 17 30 & f_{1} 50 & 32 70 & f_{2} 90 & 19 Total & 120 \end{matrix}$

Number of accidents (x):	0	1	2	3	4	5	Total
Frequency (f):	46	?	?	25	10	5	200

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Class	Frequency $(x_{i})$	$(f_{i})$	$(f_{i} x_{i})$
0-10 10-20 20-30 30-40 40-50	12 16 6 f 9 __________ 43+f	5 15 25 35 45	60 240 150 35 f 405 _________ 855+35 f