Five numbers — min, Q1, median, Q3, max — and a little box-with-whiskers picture. That's enough to compare two whole datasets in one glance. Statisticians' favourite shorthand.
A box plot (box-and-whisker plot) summarises a dataset with its five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), maximum. The box spans the middle 50%.
Comparing groups (test scores by class, salaries by department), spotting skew, flagging outliers — all at a glance, side by side.
Anatomy of a box plot
- Box — from Q1 to Q3 (the middle 50%, the interquartile range).
- Line in the box — the median.
- Whiskers — extend to the furthest points within 1.5 × IQR.
- Dots beyond whiskers — outliers worth investigating.
Two classes' test scores as box plots: Class A's box is narrow and high; Class B's box is wide and lower. What's the takeaway?
What's the IQR and why does it matter?
IQR = Q3 − Q1 = the width of the box = the spread of the middle 50%. Unlike the range, it ignores outliers, so it's a robust measure of spread.
A box plot hides the shape within each quarter. Two very different distributions can have identical box plots. For shape detail, pair it with a histogram.
Box plots shine for comparing many groups — line up 10 box plots and rankings, spreads, and outliers all pop out instantly.
- Shows the five-number summary; box = middle 50% (IQR).
- Median position inside the box reveals skew.
- Best tool for comparing groups side by side.