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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 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.

Median, Quartiles and Interquartile Range.

How to calculate this for discrete data.

Estimated Mean, Median and Quartiles from Continuous Grouped Data

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