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Question
The algebraic sum of the deviations of a set of n values from their mean is
The algebraic sum of the deviations of a set of n values from their mean is
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Solution
The correct option is B 0
Let A.M. of x1,x2,....xn=x1+x2+....+xnn=K
Mean deviation =∑n1(x−K)n=x1−K+x2−K+....+xn−Kn=x1+x2+....+xn−nKn=x1+x2+....+xnn−K⇒K−K=0
Hence, the algebraic sum of the deviations of a set of n values from their mean is 0
Let A.M. of x1,x2,....xn=x1+x2+....+xnn=K
Mean deviation =∑n1(x−K)n=x1−K+x2−K+....+xn−Kn=x1+x2+....+xn−nKn=x1+x2+....+xnn−K
⇒K−K=0
Hence, the algebraic sum of the deviations of a set of n values from their mean is 0
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