If $M.D.$ is $12$, the value of $S.D.$ will be

Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$ be in $A.P.$ and $a_1+a_3=10$. If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$, then $8 \sigma^2$ is equal to

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

The mean and variance of seven observations are $8$ and $16$, respectively. If $5$ of the observations are $2, 4, 10, 12, 14,$ then the product of the remaining two observations is

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

Find the mean, variance and standard deviation using short-cut method