Find the mean of the following frequency distribution:
Classes: 0-20 20-40 40-60 60-80 80-100
Frequency: 15 18 21 29 17

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Solution

Calculation of Mean
Classes Mid-values
( $x_{i}$ ) Frequency
( $f_{i}$ ) $d_{i} = x_{i} - 50$ $u_{i} = \frac{x_{i} - 50}{20}$ $f_{i} u_{i}$
0-20 10 15 -40 -2 -30
20-40 30 18 -20 -1 -18
40-60 50 21 0 0 0
60-80 70 29 20 1 29
80-100 90 17 40 2 34
$\sum f_{i} = 100$ $\sum f_{i} u_{i} = 15$
We have,
A= 50, h= 20, N= 100 and $\sum f_{i} u_{i}$ =15
$∴ M e a n = A + h [\frac{1}{N} \sum f_{i} u_{i}]$
$\Rightarrow M e a n = 50 + 20 \times \frac{15}{100}$
$\Rightarrow Mean = 50+3= 53

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a

Class	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100
Frequency	15	20	30	a	10

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

Marks	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100
Frequency	5	10	20	10	15

Class-interval	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120
Frequency	10	35	52	61	38	20

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

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

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