Given a data set that is sorted in ascending order, which statements correctly define Q1, Q3, and IQR?

• A. Q1 is the 25th percentile; Q3 is the 75th percentile; IQR = Q3 − Q1.
• B. Q1 is the 50th percentile; Q3 is the 50th percentile; IQR = Q3 − Q1.
• C. Q1 is the 25th percentile; Q3 is the 75th percentile; IQR = Q1 − Q3.
• D. Q1 is the 75th percentile; Q3 is the 25th percentile; IQR = Q3 − Q1.

Answer: (A)

Quartiles split data into quarters, and the central measure of spread for the middle half is the interquartile range. In a sorted data set, the first quartile is the 25th percentile, the third quartile is the 75th percentile, and the interquartile range is the difference between them, IQR = Q3 − Q1. This setup means 25% of observations fall at or below Q1, 75% fall at or below Q3, and the central 50% of data lie between Q1 and Q3. The statement that Q1 is the 25th percentile, Q3 is the 75th percentile, and IQR equals Q3 minus Q1 matches this interpretation.

The other options disrupt this ordering: using the 50th percentile for both Q1 and Q3 would place them at the median rather than the first and third quartiles; defining IQR as Q1 − Q3 would give a negative value; and swapping the percentiles so Q1 is at the 75th percentile and Q3 at the 25th percentile reverses the natural order.