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Quartiles—Wolfram Language Documentation

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• See Also
  • Quantile
  • InterquartileRange
  • QuartileDeviation
  • QuartileSkewness
• Related Guides
  • Date & Time
  • Survival Analysis
  • Descriptive Statistics
  • Tabular Modeling
  • Robust Descriptive Statistics
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  • Descriptive Statistics

Quartiles[data]

gives the quantile estimates of the elements in data.

Quartiles[data,{{a,b},{c,d}}]

uses the quantile definition specified by parameters a, b, c, d.

Quartiles[dist]

gives the quantiles of the distribution dist.

• is equivalent to the median. »
• is equivalent to the average of the medians of the and smallest elements in data if is odd, and the median of the smallest elements if is even.
• is defined like , but with the largest rather than smallest elements.
• For MatrixQ data, the quartile is computed for each column vector with Quartiles[{{x₁,y₁,…},{x₂,y₂,…},…}] equivalent to {Quartiles[{x₁,x₂,…}],Quartiles[{y₁,y₂,…}]}. »
• For ArrayQ data, quartiles are equivalent to ArrayReduce[Quartiles,data,1]. »
• Quartiles[data] is equivalent to Quantile[data,{1,2,3}/4,{{1/2,0},{0,1}}]. »
• Quartiles[data,{{a,b},{c,d}}] is equivalent to Quantile[data,{1,2,3}/4,{{a,b},{c,d}}].
• Common choices of parameters {{a,b},{c,d}} include:
• {{0,0},{1,0}} inverse empirical CDF {{0,0},{0,1}} linear interpolation (California method) {{1/2,0},{0,0}} element numbered closest to p n {{1/2,0},{0,1}} linear interpolation (hydrologist method; default) {{0,1},{0,1}} mean‐based estimate (Weibull method) {{1,-1},{0,1}} mode‐based estimate {{1/3,1/3},{0,1}} median‐based estimate {{3/8,1/4},{0,1}} normal distribution estimate
• The default choice of parameters is {{1/2,0},{0,1}}. »
• The data can have the following additional forms and interpretations:
• Quartiles[dist] gives the list corresponding to Quantile[dist]. »
• For a random process proc, the quartiles function can be computed for slice distribution at time t, SliceDistribution[proc,t], as Quartiles[SliceDistribution[proc,t]]. »

Quartiles for a list of exact numbers:

Quartiles of a list of dates:

Quartiles of a parametric distribution:

Exact input yields exact output:

Approximate input yields approximate output:

Compute results using other parametrizations:

Find the quartiles of WeightedData:

Find the quartiles of EventData:

Find the quartiles of TemporalData:

Find the quartiles of TimeSeries:

The quartiles depend only on the values:

Find the quartiles for data involving quantities:

Channelwise quartile values of an RGB image:

Quartile intensity values of a grayscale image:

Quartile amplitudes of all channels:

Compute quartiles of dates:

Compute the weighted quartiles of dates:

Compute the quartiles of dates given in different calendars:

The mean is given in one of the input calendars:

Compute the quartiles of times:

List of times with different time zone specifications:

Find the quartiles for a parametric distribution:

Quartiles for a derived distribution:

Data distribution:

Quartile functions for a random process:

Quartiles divide a distribution in four equal probability sections:

Find a moving quartile envelope for a time series:

Data smoothed by moving median:

Moving envelope of first and third quartiles:

Find the quartiles for data representing the top oil-producing fields in 2001:

Compare with the minimum and maximum values for the data:

Plot the data with quartile lines:

Compute the quartiles for the heights of children in a class:

Quartiles are given by linearly interpolated Quantile values:

The default parameters for Quantile give a different result:

The second quartile of the data is the Median:

The quantile of 1/2 does not average the two middle elements for lists of even length:

InterquartileRange is the difference between the first and third quartiles:

QuartileDeviation is half the difference between the first and third quartiles:

QuartileSkewness is a skewness measure obtained from the quartiles:

BoxWhiskerChart shows the quartiles for data:

Quartiles requires numeric values in data:

The symbolic closed form may exist for some distributions:

Quartiles of data computed via Quantile do not always agree with Quartiles:

Specify linear interpolation parameters in Quantile:

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