# 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.

### Three-point estimation

Three-point estimation

Seven-number summary

### 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

### List of statistics articles

**list of statistical topicslist of statistics topics**

Seven-number summary