The variance of first $50$ even natural numbers is

Let the mean and variance of the frequency distribution

be $6$ and $6.8$ respectively. If $x_{3}$ is changed from $8$ to $7 ,$ then the mean for the new data will be:

The mean and standard deviation of a group of $100$ observations were found to be $20$ and $3,$ respectively. Later on it was found that three observations were incorrect, which were recorded as $21,21$ and $18 .$ Find the mean and standard deviation if the incorrect observations are omitted.

From a lot of $12$ items containing $3$ defectives, a sample of $5$ items is drawn at random. Let the random variable $\mathrm{X}$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of $X$ is $\frac{m}{n}$, where $\operatorname{gcd}(m, n)=1$, then $n-m$ is equal to..........

If the variance of the first $n$ natural numbers is $10$ and the variance of the first m even natural numbers is $16$, then $m + n$ is equal to

Mean of $5$ observations is $7.$ If four of these observations are $6, 7, 8, 10$ and one is missing then the variance of all the five observations is