The variance of $\alpha$, $\beta$ and $\gamma$ is $9$, then variance of $5$$\alpha$, $5$$\beta$ and $5$$\gamma$ is
$45$
$9\over5$
$5\over9$
$225$
The mean and the standard deviation (s.d.) of $10$ observations are $20$ and $2$ resepectively. Each of these $10$ observations is multiplied by $\mathrm{p}$ and then reduced by $\mathrm{q}$, where $\mathrm{p} \neq 0$ and $\mathrm{q} \neq 0 .$ If the new mean and new s.d. become half of their original values, then $q$ is equal to
The means of five observations is $4$ and their variance is $5.2$. If three of these observations are $1, 2$ and $6$, then the other two are
Let $n \geq 3$. A list of numbers $0 < x_1 < x_2 < \ldots < x_n$ has mean $\mu$ and standard deviation $\sigma$. A new list of numbers is made as follows: $y_1=0, y_2=x_2, \ldots, x_{n-1}$ $=x_n-1, y_n=x_1+x_n$. The mean and the standard deviation of the new list are $\hat{\mu}$ and $\hat{\sigma}$. Which of the following is necessarily true?
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 $4\bar x$.
Let the mean and variance of $8$ numbers $x , y , 10$, $12,6,12,4,8$, be $9$ and $9.25$ respectively. If $x > y$, then $3 x-2 y$ is equal to $...........$.