A study collected subjective pain scores (scale 1–10) from 100 patients at 24 hours post-extraction without pain control. The boxplot of the data is shown. What is the interquartile range?

Correct answer: D. 4

• A. 7 is either the position of Q3 or the full range from the lower whisker (2) to a point short of the upper whisker. The whiskers describe the total spread, not the interquartile range.
• B. 3 is the value of Q1 itself — the position of the left edge of the box, not its width. A common trap: the question asks for a range, so the answer must be a difference between two values.
• C. 2 would be the distance from the lower whisker to Q1, or roughly the gap from Q1 to the median. Neither is the interquartile range.
• D. CORRECT. The interquartile range is Q3 − Q1 — the width of the BOX itself, not the whiskers. Reading the plot, the left edge of the box (Q1, 25th percentile) sits at 3 and the right edge (Q3, 75th percentile) sits at 7. IQR = 7 − 3 = 4. The IQR captures the middle 50% of the data and is a measure of SPREAD that is resistant to outliers, which is precisely why it is preferred over the range for skewed distributions like pain scores.

Note: Anatomy of a boxplot: the box spans Q1 to Q3 (the IQR); the line inside it is the MEDIAN, not the mean; the whiskers usually extend to the most extreme points within 1.5 × IQR; anything beyond is plotted as an outlier. Note the median here sits left of centre within the box — the distribution is right-skewed.