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Question

Assertion :If the mean of a set of observations x1,x2,.....,xn is ¯x, then mean of the observations xi+2;i=1,2,...,n is ¯x+2. Reason: If each observation is increased by 2, then mean is increased by 2 .

A
Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion.
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B
Both Assertion & Reason are individually true but Reason is not the correct (proper) explanation of Assertion.
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C
Assertion is true Reason is false.
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D
Assertion is false Reason is true.
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Solution

The correct option is A Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion.
Given x1+x2+...+xnn=¯x
(x1+2)+(x2+2)+(x3+2)+...+(xn+2)n
=(x1+x2+...+xn)+2nn
=x1+x2+...+xnn+2
=¯x+2
Thus Assertion (A) & Reason (R) both are correct & Reason (R) is the correct explanation of Assertion (A).

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