fivenumber

The five-number summary, sometimes called the fivenumber, is a concise statistical description of a dataset that consists of five values: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum. It provides a quick snapshot of the data’s location, spread, and symmetry.

To compute the five-number summary, the data are first ordered from smallest to largest. The minimum and maximum are the endpoints. The quartiles partition the data into quarters, with Q1 at roughly the 25th percentile and Q3 at roughly the 75th percentile. The median is the middle value (or the average of the two central values for even sample sizes). Different methods for calculating quartiles can yield slightly different results, and software packages may vary in their exact definitions.

The five-number summary is widely used in exploratory data analysis and as the basis for box plots. The spread is captured by the interquartile range (IQR) = Q3 − Q1. Box plots typically show a box spanning Q1 to Q3 with a line at the median, and whiskers extending to the minimum and maximum or to boundaries such as Q1 − 1.5·IQR and Q3 + 1.5·IQR. Observations beyond these boundaries are often labeled as outliers.

Limitations include a lack of detail about the distribution beyond min, max, and the quartiles, and potential sensitivity to the method chosen for quartile calculation. When comparing datasets, ensuring consistent quartile definitions is important for reliable interpretation. The five-number summary remains a compact, robust starting point for summarizing data, especially in skewed distributions.