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Question

Let x1, x2, ,xn be n observations, and let ¯x be their arithmetic mean and σ2 be the variance.
Statement – 1: Variance of 2x1,2x2,,2xn is 4σ2
Statement – 2: Arithmetic mean 2x1,2x2,,2xn is 4¯x


A

Statement – 1 is false, Statement – 2 is true

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B

Statement – 1 is true, statement – 2 is true; statement – 2 is a correct explanation for Statement – 1.

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C

Statement – 1 is true, statement – 2 is true; statement – 2 is not a correct explanation for Statement – 1.

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D

Statement – 1 is true, statement – 2 is false.

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Solution

The correct option is D

Statement – 1 is true, statement – 2 is false.


If each observation is multiplied by k, mean gets multiplied by k and variance gets multiplied by k2. Hence the new mean should be 2¯x and new variance should be 22σ2 .
So statement –I s true and statement – 2 is false.


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