Q.

If ASD,  AMD denotes, respectively the standard deviation and the mean deviation about mean, of the set of elements of A, then which of the following is/are true?

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a

for  A={5,7,  9,  11,  13},(ASD)<π

b

for  A={2,4,  6,  8,  10},(ASD)>(AMD)

c

for  A={2022,  2024,  2026,2028,  2030},(AMD)=2.4

d

for  A={2002,  2005,  2008,  ......,2023},(ASD)=372

answer is A, B, D.

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Detailed Solution

S.D of ‘n’ consecutive terms of an A.P with common difference d=|d|n2112

M.D from mean X¯=|xix¯|n

S.D and M.D are independent of origin

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If ASD,  AMD denotes, respectively the standard deviation and the mean deviation about mean, of the set of elements of A, then which of the following is/are true?