Box Plot

The box plot (Tukey, 1977) condenses a distribution into five numbers and thereby makes it possible to compare many groups side by side — where several histograms would need too much space.

• Box — from the lower quartile $Q_1$ to the upper quartile $Q_3$; it holds the middle 50 % of values
• Median line — the median inside the box; its position reveals skewness
• Interquartile range — $IQR=Q_3-Q_1$, the robust measure of spread
• Whiskers — out to the most extreme value within $1.5\cdot IQR$ of the box
• Outliers — anything beyond the whiskers is plotted individually

All five numbers are robust: they rest on ranks, not sums, so a single extreme value moves neither the box nor the median line. That is precisely the advantage over the mean plus standard deviation combination.