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The mean of the following data, using the assumed-mean method is ____.

Class
0-10
10-20
20-30
30-40
40-50
Frequency
7
10
15
8
10

see full answer

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Detailed Solution

The mean of the following data, using the assumed-mean method is 25.8.
Given:

Class	0-10	10-20	20-30	30-40	40-50
Frequency	7	10	15	8	10

Formula:
Mean using step deviation method:

Mean = A + h × ∑ f i u i ∑ f i where, u i = x i − A h,

A

is the assumed mean,

f

is the frequency and

h

is the size of the class of the given data.
The frequency distribution table:

Class Interval	Frequency, $f_{i}$	Mid-value, $x_{i}$	$u_{i}$ = $\frac{x_{i} - A}{h}$ = $\frac{x_{i} - 25}{10}$	$f_{i} u_{i}$
0-10	7	5	-2	-14
10-20	10	15	-1	-10
20-30	15	25=A	0	0
30-40	8	35	1	8
40-50	10	45	2	20
	Σ $f_{i}$ =50			Σ $f_{i} u_{i}$ =4

We have to find mean.
Observing from the above table:

A = 25, h = 10, ∑ f i = 50, and ∑ f i u i = 4

Substitute in formula:

M e a n = 25 + 10 × 450 M e a n = 25 + (10 × 0.08) M e a n = 25 + 0.8 M e a n = 25.8

The mean of the given data is 25.8.

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