Let ${x_1}\;,\;{x_2}\;,\;.\;.\;.\;,{x_n}$ be $n$ observations, and let $\bar x$ be their arithmaetic mean and ${\sigma ^2}$ be the variance

Statement $-1$ :Variance of $2{x_1}\;,2\;{x_2}\;,\;.\;.\;.\;,2{x_n}$ is $4{\sigma ^2}$ .

Statement $-2$: Arithmetic mean $2{x_1}\;,2\;{x_2}\;,\;.\;.\;.\;,2{x_n}$ is $4\bar x$.

  • [AIEEE 2012]
  • A

    Statement $-1$ is false, Statement $-2$ is true;

  • B

    Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not acorrect explanation for Statement $-1$

  • C

    Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is  a correct explanation for Statement $-1$

  • D

    Statement $-1$ is true, Statement $-2$ is false

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