The $S.D.$ of $15$ items is $6$. If each item is decreased or increased by $1$,then the standard deviation will be:

The outcome of each of $30$ items was observed; $10$ items gave an outcome $\frac{1}{2} - d$ each,$10$ items gave an outcome $\frac{1}{2}$ each,and the remaining $10$ items gave an outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac{4}{3}$,then $|d|$ equals:

If the total number of observations is $n = 20$,$\sum x_i = 1000$ and $\sum x_i^2 = 84000$,then the variance of the distribution is

If each of the observations $x_{1}, x_{2}, \ldots, x_{n}$ is increased by $a$,where $a$ is a positive or negative number,show that the variance remains unchanged.

The variance of $20$ observations is $5$. If each observation is multiplied by $3$ and then $8$ is added to each number,then the variance of the resulting observations is:

Calculate the variance if $\Sigma x_i^2 = 18000$ and $\Sigma x_i = 960$,for $60$ observations.