If the variance of four numbers $w, x, y,$ and $z$ is $9$,then the variance of $5w, 5x, 5y,$ and $5z$ is:

For a statistical data $x_1, x_2, \ldots, x_{10}$ of $10$ values,a student obtained the mean as $5.5$ and $\sum_{i=1}^{10} x_i^2 = 371$. He later found that he had noted two values in the data incorrectly as $4$ and $5$,instead of the correct values $6$ and $8$,respectively. The variance of the corrected data is

Let $x_1, x_2, \dots, x_n$ be $n$ observations,$\bar{x}$ be their mean,and $\sigma^2$ be their variance.
Statement-$1$: The variance of $2x_1, 2x_2, \dots, 2x_n$ is $4\sigma^2$.
Statement-$2$: The mean of $2x_1, 2x_2, \dots, 2x_n$ is $4\bar{x}$.

The $S.D.$ of $5$ scores $1, 2, 3, 4, 5$ is

If the data $x_1, x_2, ..., x_{10}$ is such that the mean of the first four of these is $11$,the mean of the remaining six is $16$,and the sum of squares of all of these is $2,000$; then the standard deviation of this data is

The arithmetic mean and standard deviation of a data set of nine numbers are $13$ and $5$ respectively. If $3$ is included as the $10^{th}$ item of the data,then the variance of the data set of ten numbers is: