Mean deviation of the series a, a + d, a + 2d, a + 2nd from its mean is Options: A . &nbsp(n+1)d(2n+1) B . &nbsp(nd)(2n+1) C . &nbspn(n+1)d(2n+1) D . &nbsp2(n+1)dn(n+1)

Answer: Option C : C ¯ x = 2 n + 1 2 ( a + a + 2 n d ) ) ( 2 n + 1 ) = a + n d ∑ | x − ¯ x | = 2 d ( 1 + 2 + . . . . . + n ) = n ( n + 1 ) d ∴ M . D = n ( n + 1 ) d ( 2 n + 1 )

Mean deviation of the series a, a + d, a + 2d, a + 2nd from its mean is

Question

Mean deviation of the series a, a + d, a + 2d, a + 2nd from its mean is

Options:

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

B . (nd)(2n+1)

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

D . 2(n+1)dn(n+1)

Answer: Option C
:
C

¯ x = \frac{\frac{2 n + 1}{2} (a + a + 2 n d))}{(2 n + 1)} = a + n d \sum | x - ¯ x | = 2 d (1 + 2 + . . . . . + n) = n (n + 1) d ∴ M . D = \frac{n (n + 1) d}{(2 n + 1)}

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