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

All students in a classroom performed poorly in mathematics. The teacher decided to increase the marks of each student by $10$. Which of the following statistical measures will not change even after adding the extra marks?

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:

If the variance of the data $2, 4, 5, 6, 8, 17$ is $23.33$,then the variance of $4, 8, 10, 12, 16, 34$ will be

Let the mean and the variance of $6$ observations $a, b, 68, 44, 48, 60$ be $55$ and $194$,respectively. If $a > b$,then the value of $a + 3b$ is:

The variance of $20$ observations is $5$. If each observation is multiplied by $2$,find the new variance of the resulting observations.