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0 votes
10.3k views
in Mathematics by (20 points)
edited by

Standard deviation of the series a, a+d , a+2d, ........, a+2nd is?

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2 Answers

+1 vote
by (10.9k points)

The given series is an AP where 1st term = a , common difference = d and number of terms = 2n+1

Hence sum of the series is S = 2n/2[2a+(2n+1-1)d]

Hence mean is m = S/2n=a+nd

So absolute value of deviations of the terms are

nd, (n-1)d,(n-2d), ....2d,..d,0, d, 2d, .....nd

Hence sum of the deviations is D= 2d(1+2+3+4+...+n)= 2dxn(n+1)/2=n(n+1)d

Hence the average deviation Dav= D/2n = (n+1)d/2

0 votes
by (323k points)

Given series

a, a+d, a+2d, ......, a+2nd

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