Mathematics

Using the step-deviation method, find the mean from the following data :
x_i f_i
18 170
19 320
20 530
21 700
22 230
23 140
24 110

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We construct the following table, taking assumed mean A = 21

Here c (width of the class) = 1

x_i	f_i	u_i = $\dfrac{(x_i - 21)}{c}$	f_iu_i
18	170	-3	-510
19	320	-2	-640
20	530	-1	-530
A = 21	700	0	0
22	230	1	230
23	140	2	280
24	110	3	330
Total	∑f_i = 2200		∑f_iu_i = -840

Mean = A + c × $\dfrac{\sum f$

= 21 + 1 × $\dfrac{-840}{2200}$

= 21 + $\dfrac{-840}{2200}$

= 21 - 0.382 = 20.62.

Hence, mean of following distribution is 20.62.

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