The mean and standard deviation of $100$ items are $50$ and $4$, respectively. Then the sum of the squares of all the items 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 $d$.

The mean of $100$ observations is $50$ and their standard deviation is $5$. Then,the sum of the squares of all the observations is:

In an experiment with $15$ observations of $x$,the results $\Sigma x^2 = 2830$ and $\Sigma x = 170$ are obtained. If one observation $20$ is found to be incorrect and is replaced by the correct observation $30$,what is the correct variance?

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-

Find the variance of the first $n$ natural numbers.