Boxplots

Boxplots, or box-and-whisker plots, are a graphical method for summarizing the distribution of a numerical variable. They display a five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The box spans from Q1 to Q3, with a line at the median. The whiskers extend from the box to show a range of data, commonly to the furthest data points within 1.5 times the interquartile range (IQR = Q3 − Q1). Data outside this range are plotted individually as outliers.

Interpretation of a boxplot focuses on the position and size of the elements. The box height reflects the IQR and thus the spread of the central 50% of values. The median line indicates central tendency; asymmetry in the box and whiskers suggests skewness. Longer whiskers on one side indicate heavier tails on that side, and outliers are shown as separate points or symbols.

Construction usually involves: computing the five-number summary, calculating the IQR, determining whisker endpoints (often the most distant data points within 1.5 IQR from the quartiles), and plotting any points outside as outliers. Notches can be added to the box to indicate an approximate confidence interval for the median in some variants.

Variants include notched boxplots, which provide median confidence intervals, and extended or adjusted boxplots that use alternative rules for whiskers or outliers. Boxplots summarize a distribution succinctly but may obscure multimodality or finer structure, and their interpretation depends on the underlying data size and the chosen whisker convention. They are widely used in exploratory data analysis and for comparing distributions across groups.