Median is defined as the middle value in a given set of numbers or data. In Mathematics, there are three different measures, which are used to find the average value for the given set of numbers. They are mean, median and mode. These three measures are called the measures of central tendency. The average value of the given data is given by mean. The middle value of the given data is defined by a median. The repeated value of the given data is defined by mode.

Here, let us discuss one of the measures called “Median” in detail. The definition of median, its formula and examples are explained.

Median Definition in Maths

In Mathematics, the median is defined as the middle value of a sorted list of numbers. The middle number is found by ordering the numbers. The numbers are ordered in the ascending order. Once the numbers are ordered, the middle number is called the median of the given data set.

Median for Odd number of Observations

It is easy to find the median for the dataset, that has an odd number of observations.

Eg. Median of 2, 5, 8 is 5

Median for Even number of Observations

If the dataset is even, then the mean value or average for the middle two numbers is called the median of the given data set.

Eg. Median of 4, 5, 6, 7 is the mean of 5 and 6, i.e.,5.5.

Median Formula

Based on the definition, the formula to find the median of the dataset is given by:

If the given number of observations/data is odd, then the formula to calculate the median is:

Median = {(n+1)/2}^th term

If the given number of observations is even, then the formula to find the median is given by:

Median = [(n/2)^th term + {(n/2)+1}^th term]/2

Where,

“n” is the number of observations.

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Solved Examples on Median

Example 1:

Determine the median for the given dataset:

5, 7, 4, 8, 6

Solution:

Given dataset: 5, 7, 4, 8, 6

Here, the number of observations is odd, i.e., 5 observations are given.

n = 5

Now, arrange the numbers in ascending order

4, 5, 6, 7, 8

The formula to calculate the median for odd observations is:

Median = {(n+1)/2}^th term

Median = {(5+1)/2}^th term

Median = 6^th term

Here, the 6^th term is 6.

Therefore, the median for the given dataset is 6.

Example 2:

Determine the median for the given dataset:

4, 7, 3, 8, 6, 2

Solution:

Given dataset: 4, 7, 3, 8, 6, 2

Here, the number of observations is even, i.e., 6 observations are given.

n = 6

Now, arrange the numbers in ascending order

2, 3, 4, 6, 7, 8

The formula to calculate the median for odd observations is:

Median = [(n/2)^th term + {(n/2)+1}^th term]/2

Median = [(6/2)^th term + {(6/2)+1}^th term]/2

Median = (3^rd term + 4^th term)/2

Here, the 3^rd term is 4 and the 4^th term is 6

Therefore, median = (4+6)/2

= 10/2 = 5

Therefore, the median for the given dataset is 5.

Practice Questions on Median

1. Find the median of 2, 8, 3, 7, 5.
2. What is the median of 65, 76, 4, 17, 68, 12, 54, 68?
3. Evaluate the median of the numbers: 6, -4, 41, 85, 50.
4. The median of 87, 56, 99, 43, 67, is?