SAT One-variable data: distributions and measures of center and spread Practice Question 6 (Medium) | SAT Owl

Question bank / One-variable data: distributions and measures of center and spread

Math · Problem-Solving and Data AnalysisMedium

	Minimum	$Q_1$	Median	$Q_3$	Maximum
Data set A	10	20	30	40	50
Data set B	5	25	30	35	70

The five-number summaries of two data sets are shown in the table. Which of the following statements is true?

A

Data set A has the greater interquartile range, and data set B has the greater range.

B

Data set A has the greater interquartile range and the greater range.

C

Data set B has the greater interquartile range and the greater range.

D

The data sets have the same interquartile range because they have the same median.

Show answer and explanation

Answer: A

The interquartile range is $Q_3 - Q_1$ : for A it is $40 - 20 = 20$ and for B it is $35 - 25 = 10$ . The range is maximum minus minimum: for A it is $50 - 10 = 40$ and for B it is $70 - 5 = 65$ . So A has the greater IQR and B has the greater range.

Choice C assumes the data set with more extreme values also has a more spread-out middle half, but B's middle $50\%$ is actually tighter.

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