The mean of $10$ observations is $16.5$. It was later noticed that one observation was taken as $57$ instead of $75$ by mistake. Find the correct mean of the data.

Find the mode of the following observations: $14, 25, 28, 29, 17, 14, 19, 22, 14, 30, 16, 28, 14, 25$.

In a diagnostic test in mathematics given to students,the following marks (out of $100$) are recorded:
$46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44$
Which 'average' will be a good representative of the above data and why?

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.

Find the median of the observations $18, 8, 12, 3, 20, 4, 10, 5$.

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.