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

Soln:

Class interval Mid value $x_{i}$ Frequency $f_{i}$ $f_{i} x_{i}$

0 – 20 10 5 50

20 – 40 30 f1 30 $f_{1}$

40 – 60 50 10 500

60 – 80 70 f2 70 $f_{2}$

80 – 100 90 7 630

100 – 120 110 8 880

N = 50 Sum = 30 $f_{1}$ + 70 $f_{2}$ + 2060

Given,
sum of frequency = 50

$5 + f_{1} + 10 + f_{2} + 7 + 8 = 50$

$f_{1} + f_{2} = 20$

$M u l t i p l y w i t h 3 o n b o t h s i d e s, 3 f_{1} + 3 f_{2} = 60 - - - - (1)$

And mean = 62.8

$\frac{S u m}{N} = 62.8$

$\frac{30 f_{1} + 70 f_{2} + 2060}{50} = 62.8$

$30 f_{1} + 70 f_{2} = 3140 - 2060 = 1080$

$3 f_{1} + 7 f_{2} = 108 - - - - (2) (D i v i d i n g b y 10)$

subtract equation (1) from equation (2)

$3 f_{1} + 7 f_{2} - 3 f_{1} - 3 f_{2} = 108 - 60$

$\Rightarrow 4 f_{2} = 48$
$\Rightarrow f_{2} = 12$
$∴$ $f_{1} + 12 = 20$
$\Rightarrow$ $f_{1} = 20 - 12$
$\Rightarrow$ $f_{1} = 8$
$∴$ $f_{1} = 8, f_{2} = 12$

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Similar questions

f_{1}

f_{2}

Class	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120	Total
Frequency	5	$f_{1}$	10	$f_{2}$	7	8	50

Class:	0−20	20−40	40−60	60−80	80−100	100−120
Frequency:	5	f₁	10	f₂	7	9

62.8

50

f_{1}

f_{2}

Class	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120
Frequency	$5$	$f_{1}$	$10$	$f_{2}$	$7$	$8$

Find the missing frequencies in the following distribution , if the sum of the frequencies is $120$ and the mean is $50$ .

$\begin{matrix} Class & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 Frequency & 17 & f_{1} & 32 & f_{2} & 19 \end{matrix}$

Classes	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120
Frequency	7	x	12	7	y	5

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