If the mean and standard deviation ($S$.$D$.) of the data $3, 5, 7, a, b$ are $5$ and $2$ respectively,then $a$ and $b$ are the roots of the equation:

Let $x_1, x_2, \ldots, x_{11}$ be the observations satisfying $\sum_{i=1}^{11}(x_i-4)=22$ and $\sum_{i=1}^{11}(x_i-4)^2=154$. If the mean and variance of the observations are $\alpha$ and $\beta$,then the quadratic equation having the roots $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ is

If the coefficients of variation of two distributions are $40$ and $20$ and their variances are $144$ and $64$ respectively,then the mean of their arithmetic means is
$(A)$ $40$
$(B)$ $12$
$(C)$ $30$
$(D)$ $35$

The mean and variance of $8$ observations are $10$ and $13.5,$ respectively. If $6$ of these observations are $5, 7, 10, 12, 14, 15,$ then the absolute difference of the remaining two observations is

The frequency distribution of the daily household expenditure of some families in a residential area is given below. If the mode of the distribution is $140$,what is the value of $b$?

Daily Expenditure (	$0-50$	$50-100$	$100-150$	$150-200$	$200-250$
Number of Families $(f)$	$24$	$33$	$37$	$b$	$25$

If $\alpha$ and $\beta$ are respectively the mean deviation about the mean and the variance of the first five prime numbers,then the ordered pair $(\alpha, \beta)$ is: