If $\sum_{i=1}^9(x_i-5)=9$ and $\sum_{i=1}^9(x_i-5)^2=45$,then the standard deviation of the nine observations $x_1, x_2, \ldots, x_9$ is

If each of the observations $x_1, x_2, \ldots, x_n$ is increased or decreased by $k$,where $k$ is a positive number,then the variance of the data:

Find the mean and variance of the frequency distribution given below:
$\begin{array}{|l|l|l|l|l|} \hline x & 1 \leq x < 3 & 3 \leq x < 5 & 5 \leq x < 7 & 7 \leq x < 10 \\ \hline f & 6 & 4 & 5 & 1 \\ \hline \end{array}$

The mean and standard deviation of a distribution of weights of a group of $20$ boys are $40 \ kg$ and $5 \ kg$ respectively. If two boys of weights $43 \ kg$ and $37 \ kg$ are excluded from this group,then the variance of the distribution of weights of the remaining group of boys is

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

The coefficient of variation and standard deviation of an ungrouped data are $60$ and $21$ respectively. If $15$ is added to every observation of the data,then the coefficient of variation of the new data is