Let x1, x2,........., xn be n observations, and let $\overline x $ be their arithematic mean and ${\sigma ^2}$ be their variance. Statement 1 : Variance of 2x1, 2x2,......., 2xn is 4${\sigma ^2}$. Statement 2 : : Arithmetic mean of 2x1, 2x2,......, 2xn is 4$\overline x $.

Question

Let x₁, x₂,........., x_n be n observations, and let $\overline x $ be their arithematic mean and ${\sigma ^2}$ be their variance.

Statement 1 : Variance of 2x₁, 2x₂,......., 2x_n is 4${\sigma ^2}$.
Statement 2 : : Arithmetic mean of 2x₁, 2x₂,......, 2x_n is 4$\overline x $.

Statement 1 is false, statement 2 is true

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

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

Statement 1 is true, statement 2 is false

Solution

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