Question

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

Answer 1

use range 3.5

Answer 2

No, but the interquartile range will be always <i>less than or equal</i> to the range.
For example:
10 <b>10</b> 14 <i>16</i> 18 <b>20</b> 20
Here the range is 20-10=10
The interquartile range is also 20-10=10.

For practical sized distributions, it is quite unlikely that equality holds, but it is a possibility.