The mean and standard deviation of $100$ items are $50$ and $4$ respectively. The sum of the squares of all the items is:

Variance of first $2n$ natural numbers 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 $\text{ mm}$)

$A$ scientist weighs $30$ fish. Their mean weight is $30 \text{ g}$ and the standard deviation is $2 \text{ g}$. Later,it is discovered that the weighing scale was not calibrated correctly and every fish's weight was recorded $2 \text{ g}$ less than the actual weight. What are the correct mean and standard deviation (in grams) of the fish weights,respectively?

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

The mean and standard deviation of marks obtained by $50$ students of a class in three subjects,Mathematics,Physics and Chemistry are given below:

Subject	Mathematics,Physics,Chemistry
Mean	$42, 32, 40.9$
Standard deviation	$12, 15, 20$

Which of the three subjects shows the highest variability in marks and which shows the lowest?