# Median

## What is median?

A median is a number that is separated by the higher half of a data sample, a population or a probability distribution, from the lower half.

### Median Meaning

The median of a set of data is the middlemost number in the set. The median is also the number that is halfway into the set. To find the median, the data should first be arranged in order from least to greatest.

For example: the median of 3, 3, 5, 9, 11 is 5. If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values: so the median of 3, 5, 7, 9 is (5+7)/2 = 6.

### How to calculate Median

To find the median, place all the numbers in value order and find the middle.

Example 1: Find the Median of 14, 63 and 55

solution: Put them in order: 14, 55, 63

The middle is 55, so the median is 55.

Example 2: Find the median of the following:

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

Solution: When we put those numbers in order we have:

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

There are fifteen numbers. Our middle is the eighth number:

The median value of this set of numbers is 24.

Example 3: Rahul’s family drove through 7 states on summer vacation. The prices of Gasoline differ from state to state. Calculate the median of gasoline cost.

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

Solution: By organizing the data from smallest to greatest, we get:

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

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