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:

If the mean of the distribution is $2.6$,then the value of $y$ is:

Variate $x$	$1$	$2$	$3$	$4$	$5$
Freq $f$ of $x$	$4$	$5$	$y$	$1$	$2$

Consider the following frequency distribution:

Class:	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Freq:	$\alpha$	$110$	$54$	$30$	$\beta$

If the sum of all frequencies is $584$ and the median is $45$,then $|\alpha-\beta|$ is equal to $.....$

For a group of $100$ students,the mean $\bar{x}_1$ and the standard deviation $\sigma_1$ of their marks were found to be $40$ and $15$ respectively. Later,it was observed that the scores $40$ and $50$ were misread as $30$ and $60$ respectively. If the mean and the standard deviation with the corrected observations of the scores are $\bar{x}_2$ and $\sigma_2$ respectively,then:

The mean of $5$ numbers is $18$. If one number is excluded,their mean becomes $16$. Then the excluded number is

Let $n \geq 3$. $A$ list of numbers $x_1, x_2, \ldots, x_n$ has mean $\mu$ and standard deviation $\sigma$. $A$ new list of numbers $y_1, y_2, \ldots, y_n$ is made as follows: $y_1 = \frac{x_1+x_2}{2}$,$y_2 = \frac{x_1+x_2}{2}$ and $y_j = x_j$ for $j = 3, 4, \ldots, n$. The mean and the standard deviation of the new list are $\hat{\mu}$ and $\hat{\sigma}$. Which of the following is necessarily true?