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 :-

From a lot of $12$ items containing $3$ defectives, a sample of $5$ items is drawn at random. Let the random variable $\mathrm{X}$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of $X$ is $\frac{m}{n}$, where $\operatorname{gcd}(m, n)=1$, then $n-m$ is equal to..........

Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution 

where $\sum f_i=62$. if $[x]$ denotes the greatest integer $\leq x$, then $\left[\mu^2+\sigma^2\right]$ is equal $.........$.

Find the mean and variance for the data $6,7,10,12,13,4,8,12$

In a series of $2n$ observations half of them equals $a$ and remaining half equals $-a$. If the standard deviation of observations is $2$ then $\left| a \right|$ equals

Find the mean, variance and standard deviation using short-cut method