If ∑i=1n(xi-a)=nand∑i=1n(xi-a)2=na,(n,a>1) then standard deviation of n observations x1,x2,x3,.......,xnis:
n(a-1)
(na-1)
(a-1)
Simplify the given equations to determine the standard deviation.
Given : ∑i=1n(xi-a)=nand∑i=1n(xi-a)2=na,(n,a>1)
The standard deviation of n observations x1,x2,x3,.......,xnis
=∑i=1n(xi-a)2n-∑i=1n(xi-a)n2=nan-nn2=(a-1)
Therefore, Option (D) is the correct answer.
The mean deviation for n observations x1,x2,....xn from their mean ¯¯¯¯¯X is given by