The variance and mean of $15$ observations are respectively $6$ and $10$. If each observation is increased by $8$,then the new variance and new mean of the resulting observations are respectively:

For the following frequency distribution,the variance is approximately equal to

Class Interval	$0$-$5$	$5$-$10$	$10$-$15$	$15$-$20$	$20$-$25$
Frequency	$4$	$1$	$10$	$3$	$2$

Which of the following sets of data has the least standard deviation?

If the variance of $x_1, x_2, \ldots, x_n$ is $\sigma_x^2$,then the variance of $\lambda x_1, \lambda x_2, \ldots, \lambda x_n$ (where $\lambda \neq 0$) is:

The standard deviations of $x_i (i=1, 2, \ldots, 10)$ and $y_i (i=1, 2, \ldots, 10)$ are $a$ and $b$ respectively. $\bar{x}$ and $\bar{y}$ are the means of these two sets of observations. If $z_i = (x_i - \bar{x})(y_i - \bar{y})$ and $\sum_{i=1}^{10} z_i = c$,then the standard deviation of the observations $(x_i - y_i)$ for $i=1, 2, \ldots, 10$ is:

The mean of four observations is $3$. If the sum of the squares of these observations is $48$,then their standard deviation is