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 $4\bar x$ .
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 $4\bar x$ .
- A
Statement $-1$ is true, statement $-2$ is true and statement $-2$ is $NOT$ the correct explanation for statement $-1$
- B
Statement $-1$ is true, statement $-2$ is false
- C
Statement $-1$ is false, stateemnt $-2$ is true
- D
Statement $-1$ is true, statement $-2$ is true and statement $-2$ is correct explanation for statement $-1$
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${x_i}$
$4$
$8$
$11$
$17$
$20$
$24$
$32$
${f_i}$
$3$
$5$
$9$
$5$
$4$
$3$
$1$
Find the variance and standard deviation for the following data:
| ${x_i}$ | $4$ | $8$ | $11$ | $17$ | $20$ | $24$ | $32$ |
| ${f_i}$ | $3$ | $5$ | $9$ | $5$ | $4$ | $3$ | $1$ |