If the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$,then the variance of the data is:

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

If the variance of the numbers $9, 15, 21, \ldots, (6n+3)$ is $P$,then the variance of the first $n$ even numbers is

The mean and standard deviation of $15$ observations are found to be $8$ and $3$ respectively. On rechecking,it was found that,in the observations,$20$ was misread as $5$. Then,the correct variance is equal to......

If $x_1, x_2, ..., x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 100$,then which of the following is a possible value of $n$?

Let $x_1, x_2, \dots, x_n$ be $n$ observations,$\bar{x}$ be their mean,and $\sigma^2$ be their variance.
Statement-$1$: The variance of $2x_1, 2x_2, \dots, 2x_n$ is $4\sigma^2$.
Statement-$2$: The mean of $2x_1, 2x_2, \dots, 2x_n$ is $4\bar{x}$.