Box Plot Analysis

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Reading five-number summaries, quartiles, interquartile range, and outliers from a box plot.

A box plot is a standardized way of displaying the distribution of numeric data based on the five-number summary: the minimum, first quartile Q1, median, third quartile Q3, and maximum. The box spans Q1 to Q3, with a line at the median; whiskers extend to the extremes (or to Q1 − 1.5·IQR and Q3 + 1.5·IQR, with points beyond marked as outliers). The interquartile range IQR = Q3 − Q1 summarizes the spread of the middle 50% of the data.

Five-number summary: min, Q1, median, Q3, max; IQR = Q3 − Q1

• Data 2, 5, 6, 7, 9, 11, 14 → min=2, Q1=5, median=7, Q3=11, max=14
• IQR = 11 − 5 = 6 (middle 50% span 6 units)
• A point at 25 would lie beyond Q3 + 1.5·IQR = 20 → outlier

How to recognize it

• The plot shows a box with whiskers and possibly individual outlier dots
• Questions ask about median, quartiles, range, or spread
• Side-by-side box plots compare the same summary across groups

Common mistakes

• Confusing the median line with the mean (box plots show the median, not the mean)
• Reading the whiskers as min/max when the plot uses the 1.5·IQR rule
• Treating IQR and range as the same thing

Practice guidance

Data Interpretation