Median Formula – Detailed explanation

Median Formula

There are three main measures in mathematics that are used to find the average value for a set of numbers. The terms mean median, and mode are used to describe them. The measures of central tendency are made up of these three variables. Mean is used to calculate the average value of a set of data. A median is a mathematical term that describes the middle value of a set of data by median formula. The mode determines the repeating value of the input data. The Median can be different depending on whether we have an odd number of data sets or even.  If the range of numbers is odd, the median value is the number in the middle, with the same number of numbers below and above it.

Median- Definition and Formula

The median is the value in a set of data that is in the middle. The median is a term that refers to the set’s centre point. Arrange the data in ascending order from least to greatest or descending order from the greatest to least value to obtain the median. A median is a number that divides a data sample, population, or probability distribution into upper and lower halves. Depending on the type of distribution, the median changes.

The formula to calculate the median is as below
Odd Number of values  in the data set

The median is calculated according to the following formula if there are odd numbers of values in the data set:
Median(M) =  (n+1/2)^th term

Where,
n is the number of outcomes
Even Number of values in the data set
if the number of values in the set  is even, then the median is the simple average of the middle two numbers. In calculation, the median is the simple average of the(  )^th and the ( + 1) ^th terms.

Examples of Median

Example1: Calculate the median for the given dataset:

15, 27, 24,18, 26

Solution:
Given data : 15, 27, 24,18, 26
Here, the number of data  is odd, i.e., 5.
n = 5

Let us first  arrange the numbers in ascending order
15,18,24,26,27
The formula to calculate the median for odd outcomes is:
Median = ^th

Median =

Median = 3^rd  term
Here, the 3^rd  term  is 24.
Therefore, the median for the given dataset is 24

Example 2: For  this collection of data 3, 6, 90, 41, 65, 32, 13, 22, 91, 102. Calculate the median.
Solution:
Given: 3, 6, 90, 41, 65, 32, 13, 22, 91, 102
First arrange the set in ascending order:
The data set will become 3, 6,13,22,32,41,65,90,91,102
We know here number of values in this set  is 10
We know Median  = ^th= = 5.5

This comes between 5^th and 6^th term

Now from the data set 5^th term= 32 and 6^th term = 41

Now add both these numbers and divide by 2 you will get the median

Median =  =  =36.5

Therefore the median value of this data set is 36.5.

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