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The mean marks per student, using assumed-mean method will be ____.

Class
0-20
20-40
40-60
60-80
80-100
100-120
Frequency
20
35
52
44
38
31

see full answer

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Detailed Solution

The mean marks per student, using assumed-mean method will be 62.55.
Given:

Class	0-20	20-40	40-60	60-80	80-100	100-120
Frequency	20	35	52	44	38	31

Formula:

Mean = A + ∑ f i d i ∑ f i

, where

A

is the assumed mean,

f

is the frequency and

d

is the mean deviation of the given data.
We have to find the mean of the following frequency distribution using the step-deviation method. Let

A = 50

be the assumed mean. The frequency and deviation table will be

Marks	Frequency ( $f_{i}$ )	Mid-value ( $x_{i}$ )	Deviation, $d_{i}$ = $x_{i}$ -A	$f_{i} d_{i}$
0-20	20	10	-40	-800
20-40	35	30	-20	-700
40-60	52	50=A	0	0
60-80	44	70	20	880
80-100	38	90	40	1520
100-120	31	110	60	1860
	Σ $f_{i}$ =220			Σ $f_{i} d_{i}$ =2760

Observing from the above table:

A = 50, ∑ f i = 220, ∑ f i d i = 2760

Substituting the values in formula:

M e a n = 50 + 2760220 M e a n = 50 + 12.55 M e a n = 62.55

Hence, the mean of the given data is 62.55.

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