# 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.

### Three-point estimation

Three-point estimation

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**

### Mid-range

**midsummarymidrangehalf-range**

### 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.

### List of statistics articles

**list of statistical topicslist of statistics topics**

Five-number summary