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 Let a,b,c,d and e be the observations with mean m and standard deviation s . The standard deviation of the  observations a+k,b+k,c+k,d+k and e+k is 

a
s
b
ks
c
s + k
d
sk

detailed solution

Correct option is A

Given observations are a,b,c,d and e .  Mean =m=a+b+c+d+e5Σxi=a+b+c+d+e=5mMean of new observations =a+k+b+k+c+k+d+k+e+k5=(a+b+c+d+e)+5k5=m+k∴ S.D. =∑xi2+k2+2kxin−m2+k2+2mk          =Σxi2n−m2+2kΣxin−2mk              =Σxi2n−m2+2km−2mk ∵Σxin=m=Σxi2n−m2=s

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