The mean of $100$ observations is $45$. It was later found that two observations $19$ and $31$ were incorrectly recorded as $91$ and $13$. The correct mean is...

Find the least positive value of $k$,if the range of $15, 14, k, 25, 30, 35$ is $23$.

If the mean and variance of six observations $7, 10, 11, 15, a, b$ are $10$ and $\frac{20}{3}$ respectively,then the value of $|a-b|$ is equal to:

For a frequency distribution,the $7^{th}$ decile is computed by the formula:

If for some $x \in R^{+} \cup \{0\}$,the frequency distribution of the marks obtained by $20$ students in a test is given by the table below,then find the mean of the marks.

Marks:	$2$	$3$	$5$	$7$
Frequency:	$(x+1)^2$	$2x-5$	$x^2-3x$	$x$

The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking,it was found that an observation $8$ was incorrect. If the incorrect observation $8$ is replaced by $12$,calculate the correct mean and standard deviation.