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Manipal MET2015MathematicsStatistics

The mean deviation from the mean of the series a, a+d, a+2 d, , a+2 n d , is

Options

  1. An(n+1) d
  2. Bn(n+1) d 2 n+1
  3. Cn_i(n+1) d 2 n
  4. Dn(n-1) d 2 n+1

Correct answer

B. n(n+1) d 2 n+1

Step-by-step solution

The mean of the series a, a+d, a+2 d, a+2 n d aligned & is x = 1 2 n+1 [a+a+d+a+2 d+ +a+2 n d] & x = 1 2 n+1 2 n+1 2 (a+a+2 n d) =a+n d aligned Mean deviation from mean, aligned & MD = 1 2 n+1 _ r=0 ^ 2 n |(a+r d)-(a+n d)| & MD = 1 2 n+1 _ r=0 ^ 2 n |r-n| d & MD = 1 2 n+1 2 d(1+2+ +n) = n(n+1) d 2 n+1 aligned

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