# Median, Quartiles And Percentiles (Ungrouped Data)

We have learned that the median is the middle value when a set of data is arranged in order of increasing magnitude. We will now consider lower quartiles and upper quartiles.

The **median** divides the data into a lower half and an upper half.

The **lower quartile** is the middle value of the lower half.

The **upper quartile **is the middle value of the upper half.

In this lesson, we will learn how to find the median, quartiles and percentiles of ungrouped data (discrete data).

Related Topics: More Lessons on Statistics

## Find Median, Quartiles and Percentiles

* ***Example*** : *
Find the median, lower quartile and upper quartile of the following numbers.

12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25

* Solution: *

First, arrange the data in ascending order:

Median (middle value) = 22

Lower quartile (middle value of the lower half) = 12

Upper quartile (middle value of the upper half) = 36

If there is an even number of data items, then we need to get the average of the middle numbers.

** *** Example: *

Find the median, lower quartile, upper quartile, interquartile range and range of the following numbers.

12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25, 65

* Solution: *

First, arrange the data in ascending order:

** Lower quartile** or **first quartile** =

** Median** or **second quartile** =

** Upper quartile** or **third quartile** =

** Interquartile range** = Upper quartile – lower quartile

= 39 – 13 = 26

** Range** = largest value – smallest value

= 65 – 5 = 60

When evaluating the quartiles, always remember to first arrange the data in increasing order.

## Videos

This video shows how to compute the interquartile range for a set of data. Remember to reorganize the data so that you can find the median values easier.

Median, Quartiles and Interquartile Range.

How to calculate this for discrete data.

Median and Quartiles from Discrete Data

Estimated Mean, Median and Quartiles from Continuous Grouped Data