The sum of $100$ observations and the sum of their squares are $400$ and $2475$,respectively. Later on,three observations,$3, 4$ and $5$,were found to be incorrect. If the incorrect observations are omitted,then the variance of the remaining observations is

The diameters of circles (in mm) drawn in a design are given below:

Diameters	$33-36$	$37-40$	$41-44$	$45-48$	$49-52$
No. of circles	$15$	$17$	$21$	$22$	$25$

Calculate the standard deviation and mean diameter of the circles.
[ Hint : First make the data continuous by making the classes as $32.5-36.5, 36.5-40.5, 40.5-44.5, 44.5-48.5, 48.5-52.5$ and then proceed.] (in $\text{ mm}$)

If the standard deviation of the numbers $2, 3, a$,and $11$ is $3.5$,then which of the following is true?

If each of given $n$ observations is multiplied by a certain positive number $k$,then for the new set of observations -

The standard deviations of two sets of observations $X=\{x_i\}$ and $Y=\{y_i\}$ $(i=1, 2, \ldots, 100)$ are respectively $5$ and $6$. If $\bar{x}, \bar{y}$ are their means and $\sum_{i=1}^{100}(x_i-\bar{x})(y_i-\bar{y})=600$,then the standard deviation of $Z=\{z_i \mid z_i=x_i-y_i\}$ is

The variance of the data $2, 3, 5, 11, 13, 17, 19$ is nearly