Mathematics

Using step deviation method, calculate the mean marks of the following distribution.
Class interval Frequency
50 - 55 5
55 - 60 20
60 - 65 10
65 - 70 10
70 - 75 9
75 - 80 6
80 - 85 12
85 - 90 8

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Let assumed mean (A) be 67.5 and i = 5.

Class interval	Frequency (f)	Class mark (x)	d = x - A	t = (x - A)/i	ft
50 - 55	5	52.5	-15	-3	-15
55 - 60	20	57.5	-10	-2	-40
60 - 65	10	62.5	-5	-1	-10
65 - 70	10	67.5	0	0	0
70 - 75	9	72.5	5	1	9
75 - 80	6	77.5	10	2	12
80 - 85	12	82.5	15	3	36
85 - 90	8	87.5	20	4	32
Total	Σf = 80				Σft = 24

n = Σf = 80.

By formula,

Mean = A + $\dfrac{Σft}{n} \times i$

= 67.5 + $\dfrac{24}{80} \times 5$

= 67.5 + $\dfrac{120}{80}$

= 67.5 + 1.5

= 69

Hence, mean = 69.

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