The mean of the $10$ observations is $68$. If each observation is divided by $2$ and then $6$ is added to each result, find the mean of the new observations so obtained.

If $\bar{x}$ represents the mean of $n$ observations $x_{1}, x_{2}, \ldots, x_{n},$ then the value of $\sum_{i=1}^{n}(x_{i}-\bar{x})$ is

The observations $56, 58, 63, x-5, x+1, 75, 81, 85$ have been arranged in ascending order. If the median of the data is $67$,find the value of $x$.

Heights (in $cm$) of $30$ girls of Class $IX$ are given below:
$140, 140, 160, 139, 153, 153, 146, 150, 148, 150, 152$
$146, 154, 150, 160, 148, 150, 148, 140, 148, 153, 138$
$152, 150, 148, 138, 152, 140, 146, 148$
Prepare a frequency distribution table for this data.

If each observation of the data is increased by $5,$ then their mean

For the following data,draw a frequency polygon:

Class	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$1$	$4$	$5$	$10$	$5$	$4$	$1$