The arithmetic mean of the observations $10, 8, 5, a, b$ is $6$ and their variance is $6.8$. Then $ab$ is equal to:

The variance of the variates $112, 116, 120, 125, 132$ about their $A.M.$ is

The marks obtained by students $A$ and $B$ in $3$ examinations are given below:
| | Exam $1$ | Exam $2$ | Exam $3$ |
|---|---|---|---|
| Marks of $A$ | $30$ | $20$ | $40$ |
| Marks of $B$ | $70$ | $0$ | $5$ |
The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is:

Consider $10$ observations $x_1, x_2, \ldots, x_{10}$ such that $\sum_{i=1}^{10}(x_i-\alpha)=2$ and $\sum_{i=1}^{10}(x_i-\beta)^2=40$,where $\alpha, \beta$ are positive integers. Let the mean and the variance of the observations be $\frac{6}{5}$ and $\frac{84}{25}$ respectively. The value of $\frac{\beta}{\alpha}$ is equal to :

The standard deviation of the numbers $31, 32, 33, \ldots, 46, 47$ is

If the coefficient of variation and variance of a frequency distribution are $7.2$ and $3.24$ respectively,then its mean is