The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency $f_{1}$ and $f_{2}$ .
Class 0-20 20-40 40-60 60-80 80-100 100-120
Frequency 5 $f_{1}$ 10 $f_{2}$ 7 8

5, 8

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6, 12

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8, 11

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8, 12

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Solution

The correct option is D $8, 12$

Class

Frequency(f)

ClassMark (x)

fx

0-20

5

10

50

20-40

$f_{1}$

30

$30 f_{1}$

40-60

10

50

500

60-80

$f_{2}$

70

$70 f_{2}$

80-100

7

90

630

100-120

8

110

880

Total

$30 + f_{1} + f_{2}$

$2060 + 30 f_{1} + 70 f_{2}$

Given $30 + f_{1} + f_{2} = 50$
$=> f_{1} + f_{2} = 20$ -- (1)
Given, Mean $= \frac{\sum f x}{\sum f} = 62.8$
$=> \frac{2060 + 30 f_{1} + 70 f_{2}}{30 + f_{1} + f_{2}} = 62.8$
$=> 2060 + 30 f_{1} + 70 f_{2} = 1884 + 62.8 f_{1} + 62.8 f_{2}$
$32.8 f_{1} - 7.2 f_{2} = 176$
=> $8.2 f_{1} - 1.8 f_{2} = 44$
=> $4.1 f_{1} - 0.9 f_{2} = 22$ -- (2)
Solving both equations 1, 2, we get
$f_{1} = 8, f_{2} = 12$

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Class	Frequency(f)	ClassMark (x)	fx
0-20	5	10	50
20-40	$f_{1}$	30	$30 f_{1}$
40-60	10	50	500
60-80	$f_{2}$	70	$70 f_{2}$
80-100	7	90	630
100-120	8	110	880
Total	$30 + f_{1} + f_{2}$		$2060 + 30 f_{1} + 70 f_{2}$

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The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency $f_{1}$ and $f_{2}$ .
Class 0-20 20-40 40-60 60-80 80-100 100-120
Frequency 5 $f_{1}$ 10 $f_{2}$ 7 8