If the variance of the following frequency distribution is $50$,then $x$ is equal to:

Class	$10-20, 20-30, 30-40$
Frequency	$2, x, 2$

The mean of two samples of size $200$ and $300$ were found to be $25$ and $10$ respectively. Their standard deviations $(S.D.)$ are $3$ and $4$ respectively. Then,the variance of the combined sample of size $500$ is:

If the mean and standard deviation of $n$ observations $x_1, x_2, \dots, x_n$ are $\bar{x}$ and $\sigma$ respectively,then what is the sum of the squares of the observations?

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 variance of $20$ observations is $5$. If each of the observations is multiplied by $2$,then the variance of the resulting observations is:

For $10$ observations $x_1, x_2, ..., x_{10}$, if $\sum_{i=1}^{10} (x_i + 2)^2 = 180$ and $\sum_{i=1}^{10} (x_i - 1)^2 = 90$, then their standard deviation is: