Five-number summary

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

sample maximumsample minimumMaximum
1) the sample minimum (smallest observation)
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
2) the lower quartile or first quartile
Five-number summary

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
Seven-number 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.
Five-number summary

Descriptive statistics

descriptivedescriptive statisticstatistics
The five-number summary is a set of descriptive statistics that provide information about a dataset.

Percentile

percentiles50th percentile85th percentile speed
It consists of the five most important sample percentiles:

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

quantitativescaleinterval scale
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

averagesample medianmedian-unbiased estimator
3) the median (the middle value)

Probability distribution

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

Order statistic

order statisticsorderedth-smallest of items
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

midsummarymidrangehalf-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 SystemSol system
This example calculates the five-number summary for the following set of observations: 0, 0, 1, 2, 63, 61, 27, 13.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 Enterprise MinerSAS Software
You can use in SAS (software) to get the five number summary:

John Tukey

TukeyTukey, JohnJohn W. 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.

Plot (graphics)

plotdata plotplots
Box plot : In descriptive statistics, a boxplot, also known as a box-and-whisker diagram or plot, is a convenient way of graphically depicting groups of numerical data through their five-number summaries (the smallest observation, lower quartile (Q1), median (Q2), upper quartile (Q3), and largest observation). A boxplot may also indicate which observations, if any, might be considered outliers.