The variance of the numbers $8,21,34,47, \ldots, 320$, is______

Mean and standard deviation of 100 items are 50 and $4,$ respectively. Then find the sum of all the item and the sum of the squares of the items.

The variance of $10$ observations is $16$. If each observation is doubled, then standard deviation of new data will be -

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

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.]

Let in a series of $2 n$ observations, half of them are equal to $a$ and remaining half are equal to $-a.$ Also by adding a constant $b$ in each of these observations, the mean and standard deviation of new set become $5$ and $20 ,$ respectively. Then the value of $a^{2}+b^{2}$ is equal to ....... .

If the mean of the data : $7, 8, 9, 7, 8, 7, \mathop \lambda \limits^. , 8$ is $8$, then the variance of this data is