The mean and variance of $20$ observations are found to be $10$ and $4,$ respectively. On rechecking,it was found that an observation $9$ was incorrect and the correct observation was $11$. Then the correct variance is

The mean of five observations is $4$ and their variance is $5.2$. If three of these observations are $1, 2$ and $6$,then the other two are

The average weight of students in a class of $35$ students is $40 \ kg$. If the weight of the teacher is included,the average weight increases by $0.5 \ kg$. The weight of the teacher is.....$kg$.

$A$ market with $3900$ operating firms has the following distribution for firms arranged according to various income groups of workers. If a histogram for the above distribution is constructed,the highest bar in the histogram would correspond to the class:

Income group	No. of firms
$150-300$	$300$
$300-500$	$500$
$500-800$	$900$
$800-1200$	$1000$
$1200-1800$	$1200$

There are $n$ observations and all of them are negative numbers. The ascending order of these observations is $x_1, x_2, \ldots, x_n$. If the signs of the first term and last term in that order are changed,then the range of the data is

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 $x$	$4$	$5$	$y$	$1$	$2$