The mean of the $10$ observations is $11$. If one new observation is included,their mean becomes $12$. The included new observation is ........

The mean of $35$ observations is $42$. Find the sum of those observations $\left(\Sigma f_{i} x_{i}\right)$.

$A$ football player scored the following number of goals in $10$ matches:
$1, 3, 2, 5, 8, 6, 1, 4, 7, 9$
Since the number of matches is $10$ (an even number),the median is calculated as:
Median $= \frac{5^{\text{th}} \text{ observation} + 6^{\text{th}} \text{ observation}}{2}$
$= \frac{8 + 6}{2} = 7$
Is this the correct answer? If not,why?

Mean of $50$ observations was found to be $80.4$. But later on,it was discovered that $96$ was misread as $69$ at one place. Find the correct mean.

The class marks of a frequency distribution are given as follows: $15, 20, 25, \ldots$ The class interval corresponding to the class mark $20$ is:

Find the mean,the median,and the mode of the observations:
$33, 92, 55, 90, 35, 77, 58, 41, 80, 64, 46$