The interquartile range is defined as Q3 minus Q1. Which of the following is true about this statistic?

The interquartile range is defined as Q3 minus Q1. Which of the following is true about this statistic?

• A. IQR equals Q3 minus Q1
• B. IQR equals Q2 minus Q1
• C. IQR equals Q3 plus Q1
• D. IQR equals Q4 minus Q2

Answer: (A)

The main point is that the interquartile range measures the spread of the middle half of the data. It is defined as the difference between the third quartile and the first quartile, so IQR = Q3 − Q1. This captures how wide the central portion of the distribution is and is robust to extreme values because it ignores the tails beyond the first and third quartiles. It’s not tied to the median or to any sums or to other quartiles in the same way, so only subtracting Q1 from Q3 reflects the central spread.

The main point is that the interquartile range measures the spread of the middle half of the data. It is defined as the difference between the third quartile and the first quartile, so IQR = Q3 − Q1. This captures how wide the central portion of the distribution is and is robust to extreme values because it ignores the tails beyond the first and third quartiles. It’s not tied to the median or to any sums or to other quartiles in the same way, so only subtracting Q1 from Q3 reflects the central spread.