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:

Determine the mean and standard deviation of the first $n$ terms of an $A.P.$ whose first term is $a$ and common difference is $d$.

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

The average marks of $10$ students in a class was $60$ with a standard deviation of $4$,while the average marks of another $10$ students was $40$ with a standard deviation of $6$. If all the $20$ students are taken together,their combined standard deviation will be:

For a frequency distribution,the standard deviation is computed by applying the formula:

The variance of the discrete data $3, 4, 5, 6, 7, 8, 10, 13$ is