what is a five number summary

The five-number summary is a set of descriptive statistics that provides information about a dataset. It consists of the five most important sample percentiles: the sample minimum, the first quartile (Q1), the median, the third quartile (Q3), and the sample maximum. This summary gives information about the location (from the median), spread (from the quartiles), and range (from the sample minimum and maximum) of the observations. It is particularly useful for ordinal, interval, and ratio measurements, and it can be used to compare several sets of observations by comparing their five-number summaries. The five-number summary is often represented graphically using a boxplot and can be used to compute various L-estimators, including the interquartile range, midhinge, range, mid-range, and trimean.