Let x₁, x₂,........., x n be n observations, and let x be their arithematic mean and σ ² be their variance. Statement 1: Variance of 2x₁, 2x₂,......., 2x n is 4 σ ². Statement 2:: Arithmetic mean of 2x₁, 2x₂,......, 2x n is 4 x.

(D) Statement 1 is true, statement 2 is false

(A) Statement 1 is false, statement 2 is true

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

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

Statistics and Probability: JEE Main 2012 Mathematics question

JEE Main 2012 · Annual, Paper 1 · Q5429

JEE Main 2012Annual, Paper 1MathematicsMediumStatistics and Probability258× since 2002

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