# Box plot

**boxplotbox and whisker plotadjusted boxplotsbox plotsbox-and-whisker plotboxplots**

In descriptive statistics, a box plot or boxplot is a method for graphically depicting groups of numerical data through their quartiles.wikipedia

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### Quartile

**quartileslower quartilelower and upper quartiles**

In descriptive statistics, a box plot or boxplot is a method for graphically depicting groups of numerical data through their quartiles. Box and whisker plots quartiles, and the band inside the box is always the second quartile (the median).

This rule is employed by the TI-83 calculator boxplot and "1-Var Stats" functions.

### Outlier

**outliersconservative estimateirregularities**

Box plots may also have lines extending vertically from the boxes (whiskers) indicating variability outside the upper and lower quartiles, hence the terms box-and-whisker plot and box-and-whisker diagram. Outliers may be plotted as individual points. The spacings between the different parts of the box indicate the degree of dispersion (spread) and skewness in the data, and show outliers.

Box plots are a hybrid.

### Interquartile range

**inter-quartile rangebelowinterquartile**

In addition to the points themselves, they allow one to visually estimate various L-estimators, notably the interquartile range, midhinge, range, mid-range, and trimean.

In descriptive statistics, the interquartile range (IQR), also called the midspread or middle 50%, or technically H-spread, is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles, IQR = Q 3 − Q 1 . In other words, the IQR is the first quartile subtracted from the third quartile; these quartiles can be clearly seen on a box plot on the data.

### Descriptive statistics

**descriptivedescriptive statisticstatistics**

In descriptive statistics, a box plot or boxplot is a method for graphically depicting groups of numerical data through their quartiles.

More recently, a collection of summarisation techniques has been formulated under the heading of exploratory data analysis: an example of such a technique is the box plot.

### Seven-number summary

**Bowley's seven-figure summaryseven-figure summary**

The unusual percentiles 2%, 9%, 91%, 98% are sometimes used for whisker cross-hatches and whisker ends to show the seven-number summary.

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.

### John Tukey

**TukeyTukey, JohnJohn W. Tukey**

Since the mathematician John W. Tukey introduced this type of visual data display in 1969, several variations on the traditional box plot have been described.

John Wilder Tukey (June 16, 1915 – July 26, 2000) was an American mathematician best known for development of the FFT algorithm and box plot.

### L-estimator

**L-estimation**

In addition to the points themselves, they allow one to visually estimate various L-estimators, notably the 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.

### Medcouple

**fast algorithm**

They rely on the medcouple statistic of skewness.

Its robustness makes it suitable for identifying outliers in adjusted boxplots.

### Bagplot

**Bivariate boxplot**

Bivariate boxplot

A bagplot, or starburst plot, is a method in robust statistics for visualizing two- or three-dimensional statistical data, analogous to the one-dimensional box plot.

### Candlestick chart

**candlestickcandlestick techniquescandlestick charts**

Candlestick chart

They are visually similar to box plots, though box plots show different information.

### Violin plot

Violin plot

It is similar to a box plot with a rotated kernel density plot on each side.

### Fan chart (statistics)

**Dispersion fan diagramFan chart**

Fan chart

reports the same information about a dispersion as a box plot:

### Functional boxplot

Functional boxplot

Analogous to the classical boxplot, the descriptive statistics of a functional boxplot are: the envelope of the 50% central region, the median curve and the maximum non-outlying envelope.

### Exploratory data analysis

**explorative data analysisexploratorydata analysis**

Exploratory data analysis

Box plot

### Five-number summary

**five-number summaries**

Five-number summary

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

### Nonparametric statistics

**non-parametricnonparametricnon-parametric statistics**

Box plots are non-parametric: they display variation in samples of a statistical population without making any assumptions of the underlying statistical distribution (though Tukey's boxplot assumes symmetry for the whiskers and normality for their length).

### Statistical population

**populationsubpopulationsubpopulations**

Box plots are non-parametric: they display variation in samples of a statistical population without making any assumptions of the underlying statistical distribution (though Tukey's boxplot assumes symmetry for the whiskers and normality for their length).

### Probability distribution

**distributioncontinuous probability distributiondiscrete probability distribution**

Box plots are non-parametric: they display variation in samples of a statistical population without making any assumptions of the underlying statistical distribution (though Tukey's boxplot assumes symmetry for the whiskers and normality for their length).

### Statistical dispersion

**dispersionvariabilityspread**

The spacings between the different parts of the box indicate the degree of dispersion (spread) and skewness in the data, and show outliers.

### Skewness

**skewedskewskewed distribution**

The spacings between the different parts of the box indicate the degree of dispersion (spread) and skewness in the data, and show outliers.

### Midhinge

In addition to the points themselves, they allow one to visually estimate various L-estimators, notably the interquartile range, midhinge, range, mid-range, and trimean.

### Range (statistics)

**rangerangingsample range**

### Mid-range

**midsummarymidrangehalf-range**

### Trimean

### Median

**averagesample medianmedian-unbiased estimator**

Box and whisker plots quartiles, and the band inside the box is always the second quartile (the median).