Grace claims that the interquartile range of a data set is never equal to its range. Which type of set can be used to prove or disprove her claim?

For a set of identical elements, the minimum and maximum are equal, so the range is 0. The first and third quartiles are also equal, making the interquartile range 0 as well; this is a counterexample to Grace’s claim. Therefore, a set consisting of identical elements will disprove her claim.

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