The mean and variance of $5$ observations are $5$ and $8$ respectively. If $3$ observations are $1, 3, 5$,then the sum of cubes of the remaining two observations is

The mean and standard deviation of $100$ observations $x_1, x_2, \ldots, x_{100}$ were calculated as $40$ and $5.1$ respectively by a student who took by mistake $50$ instead of $40$ for one observation. Then the correct value of $\sum_{i=1}^{100} x_i^2=$

The mean of $6$ distinct observations is $6.5$ and their variance is $10.25$. If $4$ out of $6$ observations are $2, 4, 5$ and $7$,then the remaining two observations are:

Statement $(I)$: The range of the ungrouped data does not change even if certain intermediate observations are removed.
Statement $(II)$: The value of the mean deviation of an ungrouped data about the median is always less than or equal to the value of the mean deviation computed about any other measure of central tendency.
Statement $(III)$: For a grouped data,range is approximated as the difference between the lower limit of the largest class and the upper limit of the smallest class.

The mean of $9$ observations is $15$. If a new observation is added,the new mean becomes $16$. What is the value of the new observation?

The mean of $5$ observations is $4.4$ and their variance is $8.24$. If three of those observations are $1, 2$ and $6$,then the other two observations are: