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State true or false.

The mean of the following frequency distribution using step deviation method is 55.5.

Marks
0-15
15-30
30-45
45-60
60-75
75-90
No. of students
2
4
5
20
9
10

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True

False

answer is A.

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Detailed Solution

Given:

Marks	0-15	15-30	30-45	45-60	60-75	75-90
No. of students	2	4	5	20	9	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.
We have to find mean marks. The frequency distribution table will be:

Class interval	Frequency, fi	Mid-value, xi	ui= $\frac{x_{i} - A}{h}$ = $\frac{x_{i} - 29.5}{10}$	fiui
0-15	2	7.5	-3	-6
15-30	4	22.5	-2	-8
30-45	5	37.5	-1	-5
45-60	20	52.5=A	0	0
60-75	9	67.5	1	9
75-90	10	82.5	2	9
	Σfi=50			Σfiui=10

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

A = 52.5, h = 15, ∑ f i = 50, and ∑ f i u i = 10

Applying formula:

Mean = 52.5 + 15 × 1050 = 52.5 + 3 = 55.5

The mean marks are 55.5.
Thus, the given statement is true.
Therefore, the correct option is 1.

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