boxplot

Boxplot, also known as a box-and-whisker plot, is a graphical display of a data set’s distribution. It summarizes key statistics: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The box spans from Q1 to Q3 and contains a line denoting the median. The height of the box equals the interquartile range (IQR = Q3 − Q1). The whiskers extend to the most extreme data points within a specified range, typically 1.5 times the IQR from the quartiles; observations beyond that threshold are plotted as individual outliers.

Boxplots are useful for comparing distributions across groups, identifying skewness, dispersion, and potential outliers, and for quick visual assessment of symmetry and variability. Some boxplots include notches around the median to give a rough sense of the confidence interval for the median, enabling visual comparisons between medians. Notch size and whisker length can vary by software or convention.

Construction notes: quartiles and the IQR are computed from the data; definitions of minimum and maximum or whisker end points may differ across implementations. Boxplots require numerical data and are typically used for a single quantitative variable, possibly grouped by a categorical factor to produce side-by-side plots.

Limitations: Boxplots summarize distribution details and may conceal features such as multimodality, gaps, or finer shape. They do not convey the full distribution and can be sensitive to how outliers are treated. Despite limits, they are a common, concise tool in exploratory data analysis.