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How To Find The Median?

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The median is a term which is commonly used in statistics and is one of the ways to find the average of a data set. In layman terms, the median can be defined as the middle.

The three ways to find the average is:

• Mean: It is considered as the most common method to find the 'average'. It is calculated by adding all the numbers in the data set and divide it by the number of data points available.
• Median: It among the least common ways to find the 'average', but the best way to use when there are data sets with outliners.
• Mode: Is the number that is present most often occurring in the data set.

How To Find The Median?
There are two ways to find a median depending on the dataset that is available:

• An odd number of data: If the median is to be found for an odd number of data, you should first arrange the numbers in ascending order and then count the number of points available. The median number will be the one which is in the middle with an equal number of points on either side of the median.
• An even number of data: If the number of data points available is even, finding the number that will appear in the middle is difficult. To calculate the median, arrange the numbers then take two numbers which are in the middle add then and divide by 2. The result is the median of an even number of data points.

Example 1: To calculate the median of an athlete's training session
25.0, 26.1, 25.7, 25.6 and 25.2 secs
There are 5 recordings of the training session available. Arrange them from smaller to larger numbers. 25.0, 25.2, 25.6, 25.7, 26.1 then to find the median the following formula can be used.

Median = {(n + 1) ÷ 2}th value
= (5 + 1) ÷ 2
= 3.

So the median value is the third number in the data set which in the above example is 25.6 secs.

Example 2: If using the same example as above, another session is added 25.0, 26.1, 25.7, 25.6, 25.2 and 24.7 secs. To find the median for this dataset, arrange the numbers in ascending order and use the above formula.
24.7, 25.0, 25.2, 25.6, 25.7 and 26.1
Median = {(n + 1) ÷ 2}th value
= (6 + 1) ÷ 2
= 7 ÷ 2
= 3.5

Since the number of points is even, there is no middle value which is distinct, and the median lies between the third and the fourth value. Median is calculated as the average of two values (25.2, 25.6) which is the 3rd and 4th value in the above example.
An average = (number below a median+ number above a median)÷ 2
= (25.2+25.6)/2 = 50.8/2= 25.4
The median is 25.4 secs.

Uses of Median:

Well, everyone wonders what is the use of median in real life?  Median is mainly used to find the average of a group.  The median salary of a city or country is ascertained.  When you need to understand the average income of a country the median represents the middle of the data.

Finding the average through median is among one of the three ways to find the average in statistics.