Posted by Anonymous on .
For a set of scores, will the interquartile range always be
less than the range? Explain your answer with an example.

Math 
Ms. Sue,
Check this explanation of interquartile range.
http://www.mathwords.com/i/interquartile_range.htm
What do you think? 
Math 
Anonymous,
Wow! This is hard!
IQR=less than median  more than median
Range= highestlowest
2 5 6 9 12
Range=122=10
median=6
so
IQR=10.53.5=7
So I'm thinking yes? 
Math 
MathMate,
The 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 9260=32.
The range is 9948=51
Example 2:
65,65,65,70,75,89,89
The interquartile range is 8965=24
The range is also 8965=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,
Thanks for the help!