In a frequency distribution,if $d_i$ is the deviation of observations from $a$,and the mean is given by $\text{Mean} = a + \frac{\Sigma f_i d_i}{\Sigma f_i}$,then what is $a$?

The mean and the standard deviation of $10$ observations are $20$ and $2$ respectively. Each of these $10$ observations is multiplied by $p$ and then reduced by $q$,where $p \neq 0$ and $q \neq 0$. If the new mean and new standard deviation (s.d.) become half of the original values,then $q$ is equal to

Let the mean and variance of $8$ numbers $-10, -7, -1, x, y, 9, 2, 16$ be $\frac{7}{2}$ and $\frac{293}{4}$ respectively. Then the mean of $4$ numbers $x, y, x + y + 1, |x - y|$ is:

The average income of individuals in one group is $\bar{x}$ and the average income of another group is $\bar{y}$. If the ratio of the number of individuals in both groups is $4:3$,what is the average income of the combined group?

$A$ set of four observations has mean $1$ and variance $13$. Another set of six observations has mean $2$ and variance $1$. Then, the variance of all these $10$ observations is equal to:

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