The mean of $25$ observations is $36$. If the mean of the first $13$ observations is $32$ and the mean of the last $13$ observations is $40$,find the $13^{\text{th}}$ observation.

The following table shows a frequency distribution for the speed of cars passing through a particular spot on a highway:

Class interval $(km/h)$	Frequency
$30-40$	$3$
$40-50$	$6$
$50-60$	$25$
$60-70$	$65$
$70-80$	$50$
$80-90$	$28$
$90-100$	$14$

Draw the frequency polygon representing the above data without drawing the histogram.

The mean of $10$ observations is $52$. If $12$ is subtracted from each observation,then the mean of the new observations so obtained is:

There are $50$ numbers. Each number is subtracted from $53$ and the mean of the numbers so obtained is found to be $-3.5$. The mean of the given numbers is: (in $.5$)

The observations $7, 15, x-1, x+1, 24, 28$ have been arranged in ascending order. If the median of the data is $21$,find the value of $x$.

The mean of the data: $2, 8, 6, 5, 4, 5, 6, 3, 6, 4, 9, 1, 5, 6, 5$ is given to be $5$. Based on this information,is it correct to say that the mean of the data: $10, 12, 10, 2, 18, 8, 12, 6, 12, 10, 8, 10, 12, 16, 4$ is $10$? Give reason.