If mean and standard deviation of $5$ observations $x_1 ,x_2 ,x_3 ,x_4 ,x_5$ are $10$ and $3$, respectively, then the variance of $6$ observations $x_1 ,x_2 ,.....,x_3$ and $-50$ is equal to

The mean of two samples of size $200$ and $300$ were found to be $25, 10$ respectively their $S.D.$ is $3$ and $4$ respectively then variance of combined sample  of size $500$ is :-

If each of the observation $x_{1}, x_{2}, \ldots ., x_{n}$ is increased by $'a'$ where $a$ is a negative or positive number, show that the variance remains unchanged.

The mean and variance of the marks obtained by the students in a test are $10$ and $4$ respectively. Later, the marks of one of the students is increased from $8$ to $12$ . If the new mean of the marks is $10.2.$ then their new variance is equal to :

Find the variance of the following data: $6,8,10,12,14,16,18,20,22,24$

What is the standard deviation of the following series