# Median Definition

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.

## 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 = 6th term

Here, the 6th 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 = (3rd term + 4th term)/2

Here, the 3rd term is 4 and the 4th 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?

## Frequently Asked Questions – FAQs

### What do you mean by median?

Median is the middle value of set of numbers, when arranged in an order.

### Is median also an average?

Median is a type of average, where we find the middle value of a sequence of numbers, when arranged in order.

### How do you calculate the median?

If the given set of data is in odd number, then arrange the numbers in an order, then find the middle value to get the median.
If the given set of data is an even number, then arrange the numbers in order, then find the average of the two central values. This will be the required median.