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……….

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

Consider three observations $a, b$ and $c$ such that $b = a + c .$ If the standard deviation of $a +2$ $b +2, c +2$ is $d ,$ then which of the following is true ?

The mean and $S.D.$ of $1, 2, 3, 4, 5, 6$ is

If the variance of observations ${x_1},\,{x_2},\,……{x_n}$ is ${\sigma ^2}$, then the variance of $a{x_1},\,a{x_2}…….,\,a{x_n}$, $\alpha \ne 0$ is