Answered

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?

A. A set consisting of identical elements will prove her claim.
B. A set consisting of different elements will prove her claim.
C. A set consisting of identical elements will disprove her claim.
D. A set consisting of different elements will disprove her claim.



Answer :

GinnyAnswer

Final answer:

The interquartile range (IQR) and range of a data set can be equal under certain conditions, using examples to disprove Grace's claim about their relationship.


Explanation:

The interquartile range (IQR) is a measure of statistical dispersion, calculated as the difference between the first (Q1) and third (Q3) quartiles of a data set. On the other hand, the range of a data set is the difference between the maximum and minimum values in the set.

To disprove Grace's claim that the IQR is never equal to the range, we can look at the following example:

  1. Set A: {1, 1, 1, 1, 1}
  2. Set B: {1, 2, 3, 4, 5}

In this case, for set A, IQR = 0 and range = 0, while for set B, IQR = 3 and range = 4, showing that the IQR and range can indeed be equal under different scenarios.


Learn more about Interquartile Range vs. Range Relationship here:

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