The mean and $S.D.$ of $1, 2, 3, 4, 5, 6$ are

The variance of the first $50$ even natural numbers is

In an experiment with $15$ observations,the results were available as $\sum X^2 = 2830$ and $\sum X = 170$. One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. The corrected variance is:

For the frequency distribution:

Variate $(x)$	$x_{1}$	$x_{2}$	$x_{3} \ldots x_{15}$
Frequency $(f)$	$f_{1}$	$f_{2}$	$f_{3} \ldots f_{15}$

where $0 < x_{1} < x_{2} < x_{3} < \ldots < x_{15} = 10$ and $\sum_{i=1}^{15} f_{i} > 0$,the standard deviation cannot be:

The standard deviations of two sets of observations $X=\{x_i\}$ and $Y=\{y_i\}$ $(i=1, 2, \ldots, 100)$ are respectively $5$ and $6$. If $\bar{x}, \bar{y}$ are their means and $\sum_{i=1}^{100}(x_i-\bar{x})(y_i-\bar{y})=600$,then the standard deviation of $Z=\{z_i \mid z_i=x_i-y_i\}$ is

For a set of observations,if the coefficient of variation is $25$ and the mean is $44$,then the variance is: