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 $5$ $f_{1}$ $10$ $f_{2}$ $7$ $8$

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Solution

Given : $¯ x = 62.8$ , $Σ f_{i} = 50$

Class $x_{i}$ Frequency
$(f_{i})$ $f_{i} x_{i}$
0-20 10 5 50
20-40 30 $f_{1}$ $30 f_{1}$
40-60 50 10 500
60-80 70 $f_{2}$ $70 f_{2}$
80-100 90 7 630
100-120 110 8 880

$Σ f_{i} = 30 + f_{1} + f_{2}$ $Σ f_{i} x_{i} = 2060 + 30 f_{1} + 70 f_{2}$
$Σ f_{i} = 30 + f_{1} + f_{2}$

$50 = 30 + f_{1} + f_{2}$

$f_{1} + f_{2} = 20 ⟶ {e q}^{n} (1)$

$¯ x = \frac{Σ f_{i} x_{i}}{Σ f_{i}}$

$\Rightarrow 62.8 = \frac{2060 + 30 f_{1} + 70 f_{2}}{30 + f_{1} + f_{2}}$

$\Rightarrow 1884 + 62.8 f_{1} + 62.8 f_{2} = 2060 + 30 f_{1} + 70 f_{2}$

$\Rightarrow 62.8 f_{1} - 30 f_{1} + 62.8 f_{2} - 70 f_{2} = 2060 - 1884$

$\Rightarrow 32.8 f_{1} - 7.2 f_{2} = 176 ⟶ {e q}^{n} (2)$

On solving ${e q}^{n} (1) & (2)$ we get,
$f_{1} = 8$ and $f_{2} = 12$ .

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Class	$x_{i}$	Frequency $(f_{i})$	$f_{i} x_{i}$
0-20	10	5	50
20-40	30	$f_{1}$	$30 f_{1}$
40-60	50	10	500
60-80	70	$f_{2}$	$70 f_{2}$
80-100	90	7	630
100-120	110	8	880
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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 $5$ $f_{1}$ $10$ $f_{2}$ $7$ $8$