If the standard deviation of the numbers $2, 3, 2x$,and $11$ is $3.5$,find the possible values of $x$.

Let $x_1, x_2, \dots, x_n$ be $n$ observations such that $\sum x_i^2 = 300$ and $\sum x_i = 60$. Which of the following is a possible value for $n$?

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 a discrete data,$\frac{1}{4}$ of the observations are equal to $a$,another $\frac{1}{4}$ of the observations are equal to $-a$. Out of the remaining,half of them are equal to $b$ and the rest are equal to $-b$. If the variance of all the observations is $ab$,then:

If each observation of a raw data whose variance is $\sigma^2$ is multiplied by $\lambda$,then the variance of the new set 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?