Answer :

Let a, b, c,d,e be the observation and mean is m



Let suppose new mean be m1




M1 =m+k


Now, The standard deviation



So, The standard deviation for new observation



Now, we can compare both observation


a+k-n=a+k-(m+k)


a+k–n = a+k–m- k


a+k-n=a-m


Similary


b+k-n=b-m


c+k-n=c-m


d+k-n=d-m


e+k-n=e-m


when we substitute the values, we get,


S1 = S


Hence, The Sd is S

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