Graphical Representations of Summary Statistics for One Quantitative Variable

A boxplot draws the five-number summary to scale: a box from $Q_1$ to $Q_3$ cut at the median, whiskers to the most extreme values inside the 1.5 IQR fences, and a separate dot for each outlier beyond them. Because quartiles are percentile cuts, each of the four regions holds about a quarter of the data, so a region's length reports how far that quarter had to spread, not how many values it contains. A long upper region with the median low in the box signals right skew, and in skewed data the undrawn mean is usually found on the tail side of the median.

The traps are two families. Misreading the picture: taking the longest region for the most data, the box for "most of the data", the median line for the mean, or two matching boxplots as proof of matching shapes, when five numbers cannot show modes, gaps, or sample size. And mangling the mechanics underneath: whiskers drawn to the raw maximum past a genuine outlier, whiskers ended at the fence instead of at a data value, or quartiles and fences computed with $+1.5$ in place of $+1.5 \times \text{IQR}$.