In an experiment with $15$ observations on $x$,we have $\sum x^2 = 2830$ 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:

Find the variance of the sequence $a, a + d, a + 2d, \dots, a + 2nd$.

If for a distribution,$\Sigma(x-5)=3$ and $\Sigma(x-5)^2=43$ and the total number of observations is $18$,then the variance of the distribution is

The sum of $10$ values is $12$ and the sum of their squares is $16.9$,then their standard deviation $(S.D.)$ is

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:

The mean of a set of $10$ observations is $5$ and the standard deviation is $2\sqrt{6}$. If the mean of another set of $20$ observations is $5$ and the standard deviation is $3\sqrt{2}$,what is the standard deviation of the combined set of $30$ observations?