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The five-number summary gives information about the location (from the median), spread (from the quartiles) and range (from the sample minimum and maximum) of the observations. Since it reports order statistics (rather than, say, the mean) the five-number summary is appropriate for ordinal measurements , as well as interval and ratio measurements.
A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot. Entries in an analysis of variance table can also be regarded as summary statistics. [1]: 378
In statistics, the sample maximum and sample minimum, also called the largest observation and smallest observation, are the values of the greatest and least elements of a sample. [1] They are basic summary statistics, used in descriptive statistics such as the five-number summary and Bowley's seven-figure summary and the associated box plot.
Along with the minimum and maximum of the data (which are also quartiles), the three quartiles described above provide a five-number summary of the data. This summary is important in statistics because it provides information about both the center and the spread of the data.
Arthur Lyon Bowley used precursors of the stemplot and five-number summary (Bowley actually used a "seven-figure summary", including the extremes, deciles and quartiles, along with the median—see his Elementary Manual of Statistics (3rd edn., 1920), p. 62 [11] – he defines "the maximum and minimum, median, quartiles and two deciles" as the ...
This single number describes the general performance of a student across the range of their course experiences. [6] The use of descriptive and summary statistics has an extensive history and, indeed, the simple tabulation of populations and of economic data was the first way the topic of statistics appeared.
Consumer Price Index Summary, U.S. Bureau of Labor and Statistics. Accessed January 16, 2025. Producer Price Index News Release summary, U.S. Bureau of Labor and Statistics. Accessed January 15, 2025.
A box plot of the data set can be generated by first calculating five relevant values of this data set: minimum, maximum, median (Q 2), first quartile (Q 1), and third quartile (Q 3). The minimum is the smallest number of the data set. In this case, the minimum recorded day temperature is 57°F. The maximum is the largest number of the data set.