In an ordered data set, the interquartile range is defined as Q3 minus Q1. Which option shows this correctly?

In an ordered data set, the interquartile range is defined as Q3 minus Q1. Which option shows this correctly?

• A. Q2 - Q1
• B. Q3 - Q2
• C. Q3 - Q1
• D. Mean - Median

Answer: (C)

The interquartile range measures how spread out the middle half of the data is. To capture that spread, you look at the third quartile (the value at the 75th percentile) and the first quartile (the value at the 25th percentile) and subtract the first from the third. So the interquartile range is Q3 minus Q1. This doesn’t involve Q2, the median, because it’s about the span of the central 50%, not the distance around the center. It also isn’t mean minus median, since those are measures of location, not spread. Therefore, the expression that shows Q3 minus Q1 correctly represents the interquartile range.

The interquartile range measures how spread out the middle half of the data is. To capture that spread, you look at the third quartile (the value at the 75th percentile) and the first quartile (the value at the 25th percentile) and subtract the first from the third. So the interquartile range is Q3 minus Q1.

This doesn’t involve Q2, the median, because it’s about the span of the central 50%, not the distance around the center. It also isn’t mean minus median, since those are measures of location, not spread. Therefore, the expression that shows Q3 minus Q1 correctly represents the interquartile range.