What is the difference between range and interquartile range?

What is the difference between range and interquartile range?

• A. Range = max − min; interquartile range = Q3 − Q1 (middle 50%).
• B. Range = max; interquartile range = min.
• C. Range = average; interquartile range = standard deviation.
• D. Range = median; interquartile range = mode.

Answer: (A)

Range looks at the whole spread of the data by using the extreme values: it’s calculated as the maximum minus the minimum. Interquartile range, on the other hand, focuses on the middle half of the data. It’s the difference between the third quartile (Q3) and the first quartile (Q1), so it shows how spread out the central portion is and is less sensitive to outliers. That’s why the best description is the one that defines range as max minus min and interquartile range as Q3 minus Q1. The other options mix up these ideas—range isn’t just the maximum, IQR isn’t the minimum, and the average or standard deviation relate to different ways of summarizing spread, not these two measures.

Range looks at the whole spread of the data by using the extreme values: it’s calculated as the maximum minus the minimum. Interquartile range, on the other hand, focuses on the middle half of the data. It’s the difference between the third quartile (Q3) and the first quartile (Q1), so it shows how spread out the central portion is and is less sensitive to outliers.

That’s why the best description is the one that defines range as max minus min and interquartile range as Q3 minus Q1. The other options mix up these ideas—range isn’t just the maximum, IQR isn’t the minimum, and the average or standard deviation relate to different ways of summarizing spread, not these two measures.