Related Topics: More Lessons on Statistics

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

In these lessons, we will learn how to find the median, quartiles and percentiles of ungrouped data (discrete 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.

The following figure shows the median, quartiles and interquartile range. Scroll down the page for examples and solutions.

### How to find Median, Quartiles and Percentiles?

* ***Example*** : *

### Videos

**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 median, quartiles and interquartile range for discrete data.**How to summarize data using quartiles and interquartile range?**
**How to Estimate Mean, Median and Quartiles from Continuous Grouped Data?**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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The following figure shows the median, quartiles and interquartile range. Scroll down the page for examples and solutions.

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.

Remember to reorganize the data so that you can find the median values easier.

How to calculate median, quartiles and interquartile range for discrete data.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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