Median Definition
Median is defined as the central or middle term of any set of numbers. It is a Mathematical term used for finding the central value of any data set like Mode and Mean.
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To find the Median of the given set of numbers, you have to arrange it first in a particular order (Ascending or Descending order). Let us show you an example for better clarification.
Note:
You can read about Ascending and Descending order in detail
Example 1:
Find the media of {2, 3, 5, 7, 8, 3, 5, 2, 7}
Solution:
First, we arrange the values in Ascending order.
{2, 2, 3, 3, 5, 5, 7, 7, 8}
The middle term of this set is “5” because it is available at the central spot of the set when counted from both sides of the set. So, you can find the Median of the given set in this simplest way.
How to find the Median of the set having an odd number of digits?
To find the Median of a set with odd numbers, you only have to arrange them in order. After that, you start counting them from both sides. You will get a term in the middle of the set that will be the Median of that particular set.
Example 2:
First, we arrange the values in Ascending order.
{12, 12, 14, 13, 16, 2, 6, 7, 19, 11, 18, 10, 9}
Solution:
Let’s arrange the given set in ascending order, (you can also set it in descending order)
{2, 6, 7, 9, 10, 11, 12, 12, 13, 14, 16, 18, 19}
By counting it from both sides, we have found that “12” is the Median of the set because it exists in the center of the set which is the 7th position.
How to find the Median of the set having an even number of digits?
To find the Median of a set with an even number of digits, you have to perform an extra step. First of all, you need to arrange the set in your desired order. After that, you have to find the two middle terms of the set.
After getting the pair of numbers, you need to add them and divide by 2 to find the Median. Let us show you an example to find media of the set having even numbers of digits
Example 3:
Find the Median of the following set
{2, 3, 7, 8, 9, 10, 21, 13, 14, 16, 17, 18, 19, 21}
Solution:
Let us arrange this set in Descending order.
{2, 3, 7, 8, 9, 10, 13, 14, 16, 17, 18, 19, 21, 21}
We have 13 and 14 as the middle terms of the above set. So, we have to add them first and then divide by 2 to find the Median.
Addition of two terms = 13 + 14
Median = 27/2
Median = 13.5
What is the difference between the Mean and Median?
The median shows the exactly central term of the given set of numbers while the Mean shows the average value of the overall set instead of showing a central term.
FAQ's
What do you mean by Median?
Median means the central term of the given set of numbers. function.
Can we say the median is the average of the numbers?
Yes, we can say that it gives an approaching value of the average. But it doesn’t exactly give the value of the average of a set.
Is it compulsory to arrange numbers for finding the Median?
Yes, it is compulsory to arrange the numbers in a specific order for finding the Median.
What is the benefit of finding the median?
It is an efficient approach to reaching the central term that is useful for solving questions related to the central tendency in Statistics.
