Variance of first n natural numbers is ________.

The mean of the numbers $a, b, 8,5,10$ is 6 and the variance is $6.8$ . Then which of the following gives possible values of $a$ and $b$ ?

If for some $x \in \mathbb{R}^{+} \cup\{0\}$, the frequency distribution of the marks obtained by 20 students in a test is

then the mean of the marks is

In an experiment with 15 observations for $x$, the following results were available $\sum x^2=2830, \sum x=170$. One observation 20 was found to be wrong and was replaced by the correct value 30 . Then the corrected variance is