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Let $x_1, x_2, x_3, x_4, .......... , x_n$ be $n$ observations and let $\bar x$ be their arithmetic mean and $\sigma ^2$ be their variance.
Statement $-1$ : Variance of observations $2x_1, 2x_2, 2x_3, ......, 2x_n$ is $4\sigma ^2$ .
Statement $-2$ : Arithmetic mean of $2x _1, 2x_2, 2x_3, ......, 2x_n$ is $4\bar x$ .
Statement $-1$ is true, statement $-2$ is true and statement $-2$ is $NOT$ the correct explanation for statement $-1$
Statement $-1$ is true, statement $-2$ is false
Statement $-1$ is false, stateemnt $-2$ is true
Statement $-1$ is true, statement $-2$ is true and statement $-2$ is correct explanation for statement $-1$
Solution
If each observations is multiplied by a constant $k$ then their mean is multiplied with $k$ and their variance is multiplied by $k^2$ .
Similar Questions
From the data given below state which group is more variable, $A$ or $B$ ?
| Marks | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $60-70$ | $70-80$ |
| Group $A$ | $9$ | $17$ | $32$ | $33$ | $40$ | $10$ | $9$ |
| Group $B$ | $10$ | $20$ | $30$ | $25$ | $43$ | $15$ | $7$ |
