The mean of a data set consisting of $20$ observations is $40$. If one observation $53$ was wrongly recorded as $33$,then the correct mean will be

The mean of $n$ observations $x_{1}, x_{2}, \ldots, x_{n}$ is $\bar{x}$. If an observation $x_{q}$ is replaced by $x_{q}^{\prime}$, then the new mean is:

The mean of five observations is $4$ and their variance is $5.2$. If three of these observations are $1, 2$ and $6$,then the other two are

Let $r$ be the range and $S^2 = \frac{1}{n - 1} \sum_{i = 1}^n (x_i - \bar{x})^2$ be the variance of a set of observations $x_1, x_2, \dots, x_n$. Then:

The mean and standard deviation of the marks of $10$ students were found to be $50$ and $12$ respectively. Later,it was observed that two marks $20$ and $25$ were wrongly read as $45$ and $50$ respectively. Then the correct variance is $............$.

The mean of $5$ observations is $4.4$ and their variance is $8.24$. If three of those observations are $1, 2$ and $6$,then the other two observations are: