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December 3, 2016
Posted by **Anonymous** on Wednesday, July 29, 2009 at 11:22am.

less than the range? Explain your answer with an example.

- Math -
**Ms. Sue**, Wednesday, July 29, 2009 at 11:25amCheck this explanation of interquartile range.

http://www.mathwords.com/i/interquartile_range.htm

What do you think? - Math -
**Anonymous**, Wednesday, July 29, 2009 at 11:33amWow! This is hard!

IQR=less than median - more than median

Range= highest-lowest

2 5 6 9 12

Range=12-2=10

median=6

so

IQR=10.5-3.5=7

So I'm thinking yes? - Math -
**MathMate**, Wednesday, July 29, 2009 at 11:37amThe interquartile range is the difference between the first and the third quartiles, and is always less than

*or equal to*the range.

In normally distributed data, it is less than the range.

Example 1:

48,**60**,65,**80**,85,**92**,99

The quartiles are shown in bold, namely Q1=60, Q2=80, and Q3=92.

The interquartile range is therefore 92-60=32.

The range is 99-48=51

Example 2:

65,**65**,65,**70**,75,**89**,89

The interquartile range is 89-65=24

The range is also 89-65=24.

This is an extreme example to illustrate that it is possible to have the interquartile range equal to the range, but highly unlikely in real life. - Math -
**Anonymous**, Wednesday, July 29, 2009 at 11:42amThanks for the help!