Mathematics

Calculate the mean, by step-deviation method, for the frequency distribution given below :
Class-interval Frequency
0-5 6
5-10 14
10-15 30
15-20 48
20-25 32
25-30 16
30-35 10
35-40 4

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i = Class size = 5.

In table below,

t = $\dfrac{x - A}{i}$

Class-interval	Frequency (f)	Mid-value (x)	d = x - A	t	f × t
0-5	6	2.5	-20	-4	-24
5-10	14	7.5	-15	-3	-42
10-15	30	12.5	-10	-2	-60
15-20	48	17.5	-5	-1	-48
20-25	32	A = 22.5	0	0	0
25-30	16	27.5	5	1	16
30-35	10	32.5	10	2	20
35-40	4	37.5	15	3	12
Total	Σf = 160				Σft = -126

By formula,

Mean = A + $\dfrac{Σft}{Σf} \times i$

= 22.5 + $\dfrac{-126}{160} \times 5$

= 22.5 - $\dfrac{126}{32}$

= 22.5 - 3.9375

= 18.56

Hence, mean = 18.56

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