Using step deviation method, calculate the mean of the following frequency distribution :
Class-interval Frequency
50 – 60 9
60 – 70 11
70 – 80 10
80 – 90 14
90 – 100 8
100 – 110 12
110 – 120 11
Measures of Central Tendency
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Question

Using step deviation method, calculate the mean of the following frequency distribution :
Class-interval Frequency
50 – 60 9
60 – 70 11
70 – 80 10
80 – 90 14
90 – 100 8
100 – 110 12
110 – 120 11

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KnowledgeBoat · Accepted Answer

We construct the following table, taking assumed mean a = 85. Here, c (width of each class) = 10.

Class-interval	Frequency (f_i)	Class mark (y_i)	u_i = (y_i - a)/c	f_i u_i
50 – 60	9	55	-3	-27
60 – 70	11	65	-2	-22
70 – 80	10	75	-1	-10
80 – 90	14	a=85	0	0
90 – 100	8	95	+1	8
100 – 110	12	105	+2	24
110 – 120	11	115	+3	33
Total	∑f_i= 75			∑ f_i u_i = 6

By formula,

$\text{Mean} = a + c \times \dfrac{\sum f$

Hence, mean of the given frequency distribution is 85.8.