The standard deviation of the first $10$ multiples of $4$ is:

The standard deviation of the numbers $31, 32, 33, \ldots, 46, 47$ is

In an experiment with $15$ observations for $x$,the following results were available: $\sum x^2 = 2830$ and $\sum x = 170$. One observation $20$ was found to be wrong and was replaced by the correct value $30$. Then the corrected variance is:

The mean and standard deviation of $10$ observations are $20$ and $2$ respectively. Later on,it was observed that one observation was recorded as $50$ instead of $40$. Then the correct variance is:

Suppose values taken by a variable $x$ are such that $a \le x_i \le b$,where $x_i$ denotes the value of $x$ in the $i^{th}$ case for $i = 1, 2, ..., n$. Then:

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