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Find the mean deviation about the mean of the arithmetic progression a, a + d, a + 2d,..., a + 2nd.
- (n+1)/(2n+1) * |d|
- n(n+1)/(2n+1) * |d|
- n(n-1)/(2n+1) * |d|
- none of these
Correct answer: n(n+1)/(2n+1) * |d|
Solution
The mean is a + nd, deviations are 0, d, 2d,..., nd on each side, summing to 2*|d|*n(n+1)/2 = |d|*n(n+1); dividing by (2n+1) gives n(n+1)/(2n+1)*|d|.
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