## How to find Median

## Definition

The median of a set of data is the centre value in the set or the middlemost no in the set.

The median is also the no that is halfway into the set.

To find the median, the data should be arranged 1^{st} in ascending order or descending order i.e. order of least to greatest or greatest to the least value.

A median is a no that is separated by the higher half of the given data sample, a probability or a population distribution from the lower half.

You need to understand that the median is different for different kinds of distribution.

## Formula of Median

The formula for calculating the median of the finite no of the given data set is provided in as below.

The median formula is different for odd & even nos of observations.

Therefore, it is absolutely mandatory for recognizing 1^{st} if you have even no of values or odd no of values in the data set of numbers that is provided to you.

The formula to calculate the median of the data set is as follows.

## How to find Median for Odd No Of Observations

If the total no of observations given is odd, then the formula for calculating the median is:

Median = (n + 1) / 2 term

where n is the total no of observations

## How to find Median for Even No of Observations

If the total no of observation is even, then the median formula is:

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

where n is the total no of observations

## How to Calculate the Median?

To find the median, place all the nos (from smallest to greatest) in ascending order and find the middle no à That is the median of the given no.

## How to find Median Example1

**Q. **Find the Median of 14, 63 and 55

**A. **Put all the aforementioned nos in ascending order: 14, 55, 63

The middle no is 55, so the median is 55.

## Example 2

**Q. **Find the median of the following:

4, 17, 77, 25, 22, 23, 92, 82, 40, 24, 14, 12, 67, 23, 29

**A. **When you put those nos in the ascending order, you have:

4, 12, 14, 17, 22, 23, 23, 24, 25, 29, 40, 67, 77, 82, 92,

There are 15 nos. Our middle is the 8^{th} no:

The median value of this set of nos is 24.

## Example 3

**Q. **Rahul’s family drove through seven states on summer vacation. The prices of Gas differ from state to state. Calculate the median of gas cost.

1.79, 1.61, 2.09, 1.84, 1.96, 2.11, 1.75

**A. **By organizing the numbers in the ascending order, you get:

1.61, 1.75, 1.79, 1.84 , 1.96, 2.09, 2.11

Hence, the median of gas cost is 1.84. There are 3 states with greater gas prices and three with smaller costs.

## Frequently Asked Questions (FAQs)

What is the difference between median and mean?

Mean is the ratio of total of no of values and list of values.

**Note – **Order of the values does not even matter.

Median is defined as the centre value of an ordered list of values.

## What is the median of odd nos of observations?

The formula to find median of odd no of observations is:

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

Where n is the no of observations.

## What is the median of ten number of observations?

The median of ten nos of observations is:

**(5th term + 6th term)/2**

## What is the median of two numbers?

If the no of given set of observations is two, then you have to apply the formula of median for even no of observations, i.e.

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

For instance: Median of 15 and 20 is: [(15)+(20)]/2 = 35/2 = 17.5

## What is the Median? Give Example

It is the centre value of a given nos when the numbers are arranged in an order.

For instance, a list of observations or numbers is 33, 55, 77, 22,

Let’s arrange these numbers in ascending order, we get:

11,22,33,55,77

Hence, the median is 33.