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Let in a series of 2n observations, half of them are equal to a and remaining half are equal to –a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. Then the value of a2+b2 is equal

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a

,450

b

650

c

424

d

920

answer is C.

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Detailed Solution

Old mean=0 If each observation is added by b, mean becomes b, but given new mean =5 ∴b=5 No change in S.D due to change of origin ∴|a|=20∴a2+b2=400+25=425

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Let in a series of 2n observations, half of them are equal to a and remaining half are equal to –a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. Then the value of a2+b2 is equal