The variance of the observations $2, 3, 5, 7, 11, 13, 17, 22$ is

For a set of $50$ observations,the sum of their squares is $3050$ and their arithmetic mean is $6$. Find the standard deviation of these observations.

If $\sum_{i=1}^{5}(x_i-10)=5$ and $\sum_{i=1}^{5}(x_i-10)^2=5$,then the standard deviation of the observations $2x_1 + 7, 2x_2 + 7, 2x_3 + 7, 2x_4 + 7,$ and $2x_5 + 7$ is equal to-

The mean and variance of $n$ observations $x_1, x_2, x_3, \ldots, x_n$ are $5$ and $0$ respectively. If $\sum_{i=1}^n x_i^2 = 400$,then the value of $n$ is equal to

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:

The standard deviation of the first $n$ natural numbers is . . . . . . .