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 and variance of a set of $6$ terms are $11$ and $24$ respectively,and the mean and variance of another set of $3$ terms are $14$ and $36$ respectively. Then,the variance of all $9$ terms is equal to:

Two data sets each of size $5$ are given. If the variances are $4$ and $5$ and their corresponding means are $2$ and $4$ respectively,then what is the variance of the combined data set?

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:

Let the mean and the variance of $20$ observations $x_{1}, x_{2}, \ldots, x_{20}$ be $15$ and $9$,respectively. For $\alpha \in R$,if the mean of $(x_{1}+\alpha)^{2}, (x_{2}+\alpha)^{2}, \ldots, (x_{20}+\alpha)^{2}$ is $178$,then the square of the maximum value of $\alpha$ is equal to $...........$

The mean of a set of $30$ observations is $75$. If each observation is multiplied by a non-zero number $\lambda$ and then each of them is decreased by $25$,their mean remains the same. The value of $\lambda$ is equal to