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

use range 3.5

No, but the interquartile range will be always less than or equal to the range.
For example:
10 10 14 16 18 20 20
Here the range is 2010=10
The interquartile range is also 2010=10.
For practical sized distributions, it is quite unlikely that equality holds, but it is a possibility.