Find the mean of the following distribution by step deviation method: Class Interval 20-30 30-40 40-50 50-60 60-70 70-80 Frequency 10 6 8 12 5 9

ICSE Class X Math 2013 Solved Paper - Question 37

Question : 37 of 46

Marks: +1, -0

Find the mean of the following distribution by step deviation method:

Class Interval	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	10	6	8	12	5	9

Solution:

C.I.	Frequency $(f_i)$	Mid-value(x)	$d_i= \;{x-a}/{h}$	$f_id_i$
20-30	10	25	-2	-20
30-40	6	35	-1	-6
40-50	8	45	0	0
50-60	12	55	1	12
60-70	5	65	2	10
70-80	9	75	3	27
	$\Σf_i=50$			$\Σf_id_i=50$

Here,

a=45

and

h=10

∴ \;\; \;\text " Mean "\;=a+\;{Σ f_i d_i}/{Σ f_i} × h

\;=45+\;{23}/{50} × 10

\;=45+4.6=49.6

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