Name: Median of Grouped Data: Illustration
Uploaded: 2019-07-19
Duration: 4 min 9 s
Description: The median is the middle value in distribution when the values are arranged in ascending or descending order. Learn how to calculate the median of a frequenc...

Question

The distance covered by an athlete in long jump practice are

6.10, 6.20, 6.18, 6.20, 6.25, 6.21, 6.15, 6.10

in metres. Find the mean and median. Why is it that there is not much difference between them?

Accepted Answer

Given the distance covered by an athlete in long jump practice are $6.10, 6.20, 6.18, 6.20, 6.25, 6.21, 6.15, 6.10$ in metres.

To find the mean of the given data

We know that,

Mean of data $= \frac{Sum of the observations}{Number of observations}$

Mean of the distance covered by an athlete $= \frac{6.10 + 6.20 + 6.18 + 6.20 + 6.25 + 6.21 + 6.15 + 6.10}{8}$

$= \frac{49.39}{8}$

$= 6.17$

$∴$ Mean of the distance covered by an athlete in long jump is $6.17$ .

To find the median of the given data

The median is the middle value in the list of numbers.

Arrange the data in ascending order, we have

$6.10, 6.10, 6.15, 6.18, 6.20, 6.20, 6.21, 6.25$

When the number of terms is even, then median is the average of the two middle terms.

The two central values are ${(\frac{n}{2})}^{t h}$ and ${(\frac{n}{2} + 1)}^{t h}$ term where $n$ is the number of terms

Here, $4^{t h}$ and $5^{t h}$ terms are the middle terms.

So, average of $6.18$ and $6.20$

Median $= \frac{6.18 + 6.20}{2} = 6.19$ .

There is not much difference in the mean and median values is because both are kind of averages of the data.

Districts	Rainfall ( $mm$ )
Kasargod	$66.7$
Kannur	$56.9$
Kozhikode	$33.5$
Wayanad	$20.5$
Malappuram	$13.5$
Palakkad	$56.9$
Thrissur	$53.4$
Ernakulam	$70.6$
Kottayam	$50.3$
Idukki	$30.5$
Pathanamthitta	$56.4$
Alapuzha	$45.5$
Kollam	$56.3$
Thiruvananthapuram	$89.0$

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