Five-number summary

five-number summaries
The five-number summary is a set of descriptive statistics that provides information about a dataset.wikipedia
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Sample maximum and minimum

sample maximumsample minimumMaximum
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.

Quartile

quartileslower quartilelower and upper quartiles

L-estimator

L-estimation
In addition to the points themselves, many L-estimators can be computed from the five-number summary, including interquartile range, midhinge, range, mid-range, and trimean.
However, the simplicity of L-estimators means that they are easily interpreted and visualized, and makes them suited for descriptive statistics and statistics education; many can even be computed mentally from a five-number summary or seven-number summary, or visualized from a box plot.

Seven-number summary

Bowley's seven-figure summaryseven-figure summary
In descriptive statistics, the seven-number summary is a collection of seven summary statistics, and is an extension of the five-number summary.

Box plot

boxplotbox and whisker plotadjusted boxplots
It is possible to quickly compare several sets of observations by comparing their five-number summaries, which can be represented graphically using a boxplot.

Percentile

percentiles50th percentile85th percentile speed

Univariate

In order for these statistics to exist the observations must be from a univariate variable that can be measured on an ordinal, interval or ratio scale.

Level of measurement

quantitativelevels of measurementscale
In order for these statistics to exist the observations must be from a univariate variable that can be measured on an ordinal, interval or ratio scale. 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.

Median

Probability distribution

distributioncontinuous probability distributiondiscrete probability distribution
The five-number summary provides a concise summary of the distribution of the observations.

Order statistic

order statisticsk'th-smallest of n itemsordered
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.

Interquartile range

inter-quartile rangebelowinterquartile
In addition to the points themselves, many L-estimators can be computed from the five-number summary, including interquartile range, midhinge, range, mid-range, and trimean.

Midhinge

In addition to the points themselves, many L-estimators can be computed from the five-number summary, including interquartile range, midhinge, range, mid-range, and trimean.

Range (statistics)

rangerangingsample range
In addition to the points themselves, many L-estimators can be computed from the five-number summary, including interquartile range, midhinge, range, mid-range, and trimean.

Mid-range

Midrangemidsummaryhalf-range
In addition to the points themselves, many L-estimators can be computed from the five-number summary, including interquartile range, midhinge, range, mid-range, and trimean.

Trimean

In addition to the points themselves, many L-estimators can be computed from the five-number summary, including interquartile range, midhinge, range, mid-range, and trimean.

Solar System

outer Solar Systeminner Solar Systemouter planets
These are the number of moons of each planet in the Solar System.

R (programming language)

RR programming languageCRAN
It is possible to calculate the five-number summary in the R programming language using the function.

SAS (software)

SASSAS SystemSAS Enterprise Miner
You can use in SAS (software) to get the five number summary:

John Tukey

John W. TukeyTukeyJohn Wilder Tukey
* David C. Hoaglin, Frederick Mosteller and John W. Tukey.

Summary statistics

summary statisticSummarizationdata summarization
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.