Question

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

Answer 1

Check this explanation of interquartile range.

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

What do you think?

Answer 2

Wow! 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?

Answer 3

The interquartile range is the difference between the first and the third quartiles, and is always less than <i>or equal to</i> the range.
In normally distributed data, it is less than the range.
Example 1:
48,<b>60</b>,65,<b>80</b>,85,<b>92</b>,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,<b>65</b>,65,<b>70</b>,75,<b>89</b>,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.

Answer 4

Thanks for the help!