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.wikipedia
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Summary statistics

summary statisticSummarizationdata summarization
In descriptive statistics, the seven-number summary is a collection of seven summary statistics, and is an extension of the five-number summary.
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.

Box plot

boxplotbox and whisker plotadjusted boxplots
As with the five-number summary, it can be represented by a modified box plot, adding hatch-marks on the "whiskers" for two of the additional numbers.
The unusual percentiles 2%, 9%, 91%, 98% are sometimes used for whisker cross-hatches and whisker ends to show the seven-number summary.

Five-number summary

five-number summaries
In descriptive statistics, the seven-number summary is a collection of seven summary statistics, and is an extension of the five-number summary.
Seven-number summary

Interdecile range

The addition of the deciles allow one to compute the interdecile range, which for a normal distribution can be scaled to give a reasonably efficient estimate of standard deviation, and the 10% midsummary, which when compared to the median gives an idea of the skewness in the tails.
The interdecile range is a measure of statistical dispersion of the values in a set of data, similar to the range and the interquartile range, and can be computed from the (non-parametric) seven-number summary.

Sample maximum and minimum

sample maximumsample minimumMaximum
1) the sample minimum
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.

Descriptive statistics

descriptivedescriptive statisticstatistics
In descriptive statistics, the seven-number summary is a collection of seven summary statistics, and is an extension of the five-number summary.

Percentile

percentiles50th percentile85th percentile speed
The following percentiles are evenly spaced under a normally distributed variable:

Normal distribution

normally distributednormalGaussian
The following percentiles are evenly spaced under a normally distributed variable:

Quartile

quartileslower quartilelower and upper quartiles
3) the 25th percentile or lower quartile or first quartile Arthur Bowley used a set of non-parametric statistics, called a "seven-figure summary", including the extremes, deciles and quartiles, along with the median.

Median

averagesample medianmedian-unbiased estimator
4) the 50th percentile or median (middle value, or second quartile)

Arthur Lyon Bowley

BowleyA. L. BowleyArthur Bowley
Arthur Bowley used a set of non-parametric statistics, called a "seven-figure summary", including the extremes, deciles and quartiles, along with the median.

Nonparametric statistics

non-parametricnonparametricnon-parametric statistics
Arthur Bowley used a set of non-parametric statistics, called a "seven-figure summary", including the extremes, deciles and quartiles, along with the median.

Decile

deciles
Arthur Bowley used a set of non-parametric statistics, called a "seven-figure summary", including the extremes, deciles and quartiles, along with the median.

Mid-range

midsummarymidrangehalf-range
The addition of the deciles allow one to compute the interdecile range, which for a normal distribution can be scaled to give a reasonably efficient estimate of standard deviation, and the 10% midsummary, which when compared to the median gives an idea of the skewness in the tails.

Skewness

skewedskewskewed distribution
The addition of the deciles allow one to compute the interdecile range, which for a normal distribution can be scaled to give a reasonably efficient estimate of standard deviation, and the 10% midsummary, which when compared to the median gives an idea of the skewness in the tails.

Income inequality metrics

income inequalitywage inequalityinequality
Particularly common to compare a given percentile to the median, as in the chart at right; compare seven-number summary, which summarizes a distribution by certain percentiles.

L-estimator

L-estimation
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.

Exploratory data analysis

explorative data analysisexploratorydata analysis
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 – he defines "the maximum and minimum, median, quartiles and two deciles" as the "seven positions").

Triangular distribution

triangularright-triangle distributionTriangular Probability Density Function
Seven-number summary