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PairedHistogram
  • See Also
    • Histogram
    • PairedBarChart
    • SmoothHistogram
    • Histogram3D
    • QuantilePlot
    • ProbabilityPlot
  • Related Guides
    • Statistical Visualization
    • See Also
      • Histogram
      • PairedBarChart
      • SmoothHistogram
      • Histogram3D
      • QuantilePlot
      • ProbabilityPlot
    • Related Guides
      • Statistical Visualization

PairedHistogram[{x1,x2,…},{y1,y2,…}]

plots a paired histogram of the values xi and yi.

PairedHistogram[{x1,x2,…},{y1,y2,…}, bspec]

plots a paired histogram with bin width specification bspec.

PairedHistogram[{x1,x2,…},{y1,y2,…},bspec,hspec]

plots a paired histogram with bin heights computed according to the specification hspec.

PairedHistogram[{data11,…},{data21,…},…]

plots paired histograms for multiple datasets data1i and data2j.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data and Layouts  
Tabular Data  
Wrappers  
Styling and Appearance  
Labeling and Legending  
Options  
AspectRatio  
Axes  
AxesLabel  
Show More Show More
AxesStyle  
BarOrigin  
BarSpacing  
ChartBaseStyle  
ChartElementFunction  
ChartElements  
ChartLabels  
ChartLayout  
ChartLegends  
ChartStyle  
ColorFunction  
ColorFunctionScaling  
ImageSize  
LabelingFunction  
PerformanceGoal  
PlotTheme  
Ticks  
TicksStyle  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • Histogram
    • PairedBarChart
    • SmoothHistogram
    • Histogram3D
    • QuantilePlot
    • ProbabilityPlot
  • Related Guides
    • Statistical Visualization
    • See Also
      • Histogram
      • PairedBarChart
      • SmoothHistogram
      • Histogram3D
      • QuantilePlot
      • ProbabilityPlot
    • Related Guides
      • Statistical Visualization

PairedHistogram

PairedHistogram[{x1,x2,…},{y1,y2,…}]

plots a paired histogram of the values xi and yi.

PairedHistogram[{x1,x2,…},{y1,y2,…}, bspec]

plots a paired histogram with bin width specification bspec.

PairedHistogram[{x1,x2,…},{y1,y2,…},bspec,hspec]

plots a paired histogram with bin heights computed according to the specification hspec.

PairedHistogram[{data11,…},{data21,…},…]

plots paired histograms for multiple datasets data1i and data2j.

Details and Options

  • PairedHistogram[data1,data2] by default plots a paired histogram with equal bin widths chosen to approximate an assumed underlying smooth distribution of the values xi and yi.
  • Data for PairedHistogram can be given in the following forms:
  • {e1,e2,…}list of elements with or without wrappers
    <|k1y1,k2y2,…|>association of keys and lengths
    TimeSeries[…],EventSeries[…],TemporalData[…]time series, event series, and temporal data
    WeightedData[…],EventData[…]augmented datasets
    w[{e1,e2,…},…]wrapper applied to a whole dataset
    w[{data1,data1,…},…]wrapper applied to all datasets
  • The following bin width specifications bspec can be given:
  • nuse n bins
    {dx}use bins of width dx
    {xmin,xmax,dx}use bins of width dx from xmin to xmax
    {{b1,b2,…}}use the bins [b1,b2),[b2,b3),…
    Automaticdetermine bin widths automatically
    "name"use a named binning method
    {"Log",bspec}apply binning bspec on log transformed data
    fbapply fb to get an explicit bin specification {b1,b2,…}
  • The binning specification "Log" is taken to use the Automatic underlying binning method.
  • Possible named binning methods include:
  • "Sturges"compute the number of bins based on the length of data
    "Scott"asymptotically minimize the mean square error
    "FreedmanDiaconis"twice the interquartile range divided by the cube root of sample size
    "Knuth"balance likelihood and prior probability of a piecewise uniform model
    "Wand"one-level recursive approximate Wand binning
  • The function fb in PairedHistogram[data1,data2,fb] is applied to a list of all xi and yi and should return an explicit bin list {b1,b2,…}.
  • Different forms of histogram can be obtained by giving different bin height specifications hspec in PairedHistogram[data1,data2,bspec,hspec]. The following forms can be used:
  • "Count"number of elements in each bin
    "CumulativeCount"cumulative counts
    "SurvivalCount"survival counts
    "Probability"fraction of values lying in each bin
    "Intensity"count divided by bin width
    "PDF"probability density function
    "CDF"cumulative distribution function
    "SF"survival function
    "HF"hazard function
    "CHF"cumulative hazard function
    {"Log",hspec}log transformed height specification
    fhheights obtained by applying fh to bins and counts
  • The function fh in PairedHistogram[data1,data2,bspec,fh] is applied to two arguments: a list of bins {{b1,b2},{b2,b3},…} and corresponding list of counts {c1,c2,…}. The function should return a list of heights to be used for each of the ci.
  • Only values xi that are real numbers are assigned to bins; others are taken to be missing.
  • In PairedHistogram[{data11,…},{data21,…},…], automatic bin locations are determined by combining all the datasets data1i and data2j.
  • PairedHistogram[{…,wi[datai,…],…},{…,wj[dataj],…},…] renders the histogram elements associated with dataset datak according to the specification defined by the symbolic wrapper wk.
  • The following wrappers can be used for chart elements:
  • Annotation[e,label]provide an annotation
    Button[e,action]define an action to execute when the element is clicked
    Callout[e,label]display the element with a callout
    EventHandler[e,…]define a general event handler for the element
    Hyperlink[e,uri]make the element act as a hyperlink
    Labeled[e,…]display the element with labeling
    Legended[e,…]include features of the element in a chart legend
    Mouseover[e,over]make the element show a mouseover form
    PopupWindow[e,cont]attach a popup window to the element
    StatusArea[e,label]display in the status area when the element is moused over
    Style[e,opts]show the element using the specified styles
    Tooltip[e,label]attach an arbitrary tooltip to the element
  • PairedHistogram[Tabular[…]cspec, …] extracts and plots values from the tabular object using the column specification cspec.
  • The following forms of column specifications cspec are allowed for plotting tabular data:
  • colplot values from column col
    {col1,col2,…,coln}plot columns {col1, …, coln} as a group of values
  • PairedHistogram has the same options as Graphics, with the following additions and changes: [List of all options]
  • AspectRatio 1/GoldenRatiooverall ratio of height to width
    Axes Truewhether to draw axes
    BarOrigin Bottomorigin of histogram bars
    ChartBaseStyle Automaticoverall style for bars
    ChartElementFunction Automatichow to generate raw graphics for bars
    ChartElements Automaticgraphics to use in each of the bars
    ChartLabels Nonecategory labels for datasets
    ChartLayout Automaticoverall layout to use
    ChartLegends Nonelegends for data elements and datasets
    ChartStyle Automaticstyle for bars
    ColorFunction Automatichow to color bars
    ColorFunctionScaling Truewhether to normalize arguments to ColorFunction
    LabelingFunction Automatichow to label elements
    LegendAppearanceAutomaticoverall appearance of legends
    PerformanceGoal $PerformanceGoalaspects of performance to try to optimize
    PlotTheme $PlotThemeoverall theme for the histogram
    ScalingFunctionsNonehow to scale individual coordinates
    TargetUnitsAutomaticunits to display in the chart
  • The following settings for ChartLayout can be used to display multiple sets of data:
  • "Overlapped"show all the data overlapping
    "Stacked"accumulate the data
  • The arguments supplied to ChartElementFunction are the bin region {{xmin,xmax},{ymin,ymax}}, the bin values lists, and metadata {m1,m2,…} from each level in a nested list of datasets.
  • A list of built-in settings for ChartElementFunction can be obtained from ChartElementData["PairedHistogram"].
  • The argument supplied to ColorFunction is the height for each bin.
  • With ScalingFunctions->{sx,sy}, the x coordinate is scaled using sx etc.
  • Style and other specifications from options and other constructs in BarChart are effectively applied in the order ChartStyle, ColorFunction, Style and other wrappers, ChartElements, and ChartElementFunction, with later specifications overriding earlier ones.
  • List of all options
  • Highlight options with settings specific to PairedHistogram
  • AlignmentPointCenterthe default point in the graphic to align with
    AspectRatio1/GoldenRatiooverall ratio of height to width
    AxesTruewhether to draw axes
    AxesLabelNoneaxes labels
    AxesOriginAutomaticwhere axes should cross
    AxesStyle{}style specifications for the axes
    BackgroundNonebackground color for the plot
    BarOriginBottomorigin of histogram bars
    BaselinePositionAutomatichow to align with a surrounding text baseline
    BaseStyle{}base style specifications for the graphic
    ChartBaseStyleAutomaticoverall style for bars
    ChartElementFunctionAutomatichow to generate raw graphics for bars
    ChartElementsAutomaticgraphics to use in each of the bars
    ChartLabelsNonecategory labels for datasets
    ChartLayoutAutomaticoverall layout to use
    ChartLegendsNonelegends for data elements and datasets
    ChartStyleAutomaticstyle for bars
    ColorFunctionAutomatichow to color bars
    ColorFunctionScalingTruewhether to normalize arguments to ColorFunction
    ContentSelectableAutomaticwhether to allow contents to be selected
    CoordinatesToolOptionsAutomaticdetailed behavior of the coordinates tool
    Epilog{}primitives rendered after the main plot
    FormatTypeTraditionalFormthe default format type for text
    FrameFalsewhether to put a frame around the plot
    FrameLabelNoneframe labels
    FrameStyle{}style specifications for the frame
    FrameTicksAutomaticframe ticks
    FrameTicksStyle{}style specifications for frame ticks
    GridLinesNonegrid lines to draw
    GridLinesStyle{}style specifications for grid lines
    ImageMargins0.the margins to leave around the graphic
    ImagePaddingAllwhat extra padding to allow for labels etc.
    ImageSizeAutomaticthe absolute size at which to render the graphic
    LabelingFunctionAutomatichow to label elements
    LabelStyle{}style specifications for labels
    LegendAppearanceAutomaticoverall appearance of legends
    MethodAutomaticdetails of graphics methods to use
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotLabelNonean overall label for the plot
    PlotRangeAllrange of values to include
    PlotRangeClippingFalsewhether to clip at the plot range
    PlotRangePaddingAutomatichow much to pad the range of values
    PlotRegionAutomaticthe final display region to be filled
    PlotTheme$PlotThemeoverall theme for the histogram
    PreserveImageOptionsAutomaticwhether to preserve image options when displaying new versions of the same graphic
    Prolog{}primitives rendered before the main plot
    RotateLabelTruewhether to rotate y labels on the frame
    ScalingFunctionsNonehow to scale individual coordinates
    TargetUnitsAutomaticunits to display in the chart
    TicksAutomaticaxes ticks
    TicksStyle{}style specifications for axes ticks

Examples

open all close all

Basic Examples  (2)

Generate a paired histogram of two datasets:

Plot the probability density function of the datasets:

Cumulative distribution function:

Survival function:

Hazard function:

Cumulative hazard function:

Scope  (24)

Data and Layouts  (11)

Specify the number of bins to use:

Specify the bin width:

The bin delimiters:

The bin delimiters as an explicit list:

Use different automatic binning methods:

Use logarithmically spaced bins:

Delimit bins on integer boundaries using a binning function:

Use different height specifications:

Use a height function that accumulates the bin counts:

Bins associated with a dataset are styled the same:

Numeric values in an association are used as the y coordinates:

Numeric keys and values in an association are used as the x and y coordinates:

The weights in WeightedData are ignored:

Nonreal data is taken to be missing:

Use different layouts to display multiple datasets:

Control the origin of bars:

Tabular Data  (1)

Get tabular data:

Compare the distribution of cars' miles per gallon (mpg) consumption between city and highway:

Use bins that are 5 mpg wide:

Wrappers  (2)

Use wrappers on individual data, datasets, or collections of datasets:

Wrappers can be nested:

Override the default tooltips:

Use PopupWindow to provide additional drilldown information:

Button can be used to trigger any action:

Styling and Appearance  (4)

Use an explicit list of styles for the bars:

Use any gradient or indexed color schemes from ColorData:

ChartBaseStyle can be used to set an initial style for all chart elements:

Use built-in programmatically generated bars:

For detailed settings, use Palettes ▶ ChartElementSchemes:

Labeling and Legending  (6)

Use symbolic positions to label the datasets:

Provide value labels for bars by using LabelingFunction:

Use Placed to control placement and formatting:

Add categorical legend entries for datasets:

Apply legends at different levels:

Use Placed to affect the positioning of legends:

Options  (68)

AspectRatio  (1)

By default, PairedHistogram uses a fixed height-to-width ratio for the plot:

Make the height the same as the width with AspectRatio1:

AspectRatioAutomatic determines the ratio from the plot ranges:

Axes  (3)

By default, axes are drawn:

Draw no axes:

Turn each axis on individually:

AxesLabel  (3)

No axes labels are drawn by default:

Place a label on the axis:

Use units as labels:

AxesStyle  (4)

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

Use different styles for the labels and the axes:

BarOrigin  (1)

Change the bar origin:

BarSpacing  (3)

Use automatically determined spacing between paired bars:

Use no spacing:

Use explicit spacing between bar pairs:

ChartBaseStyle  (5)

Use ChartBaseStyle to style bars:

ChartBaseStyle combines with ChartStyle:

ChartBaseStyle combines with Style:

ChartBaseStyle combines with ColorFunction:

ColorFunction may override settings for ChartBaseStyle:

Style may override settings for ChartBaseStyle:

ChartElementFunction  (5)

Get a list of built-in settings for ChartElementFunction:

For detailed settings, use Palettes ▶ ChartElementSchemes:

This ChartElementFunction is appropriate to show the global scale:

Write a custom ChartElementFunction:

Built-in element functions may have options; use Palettes ▶ ChartElementSchemes to set them:

ChartElements  (8)

Create a pictorial chart based on any Graphics object:

Graphics3D:

Image:

Use a stretched version of the graphic:

Use explicit sizes for width and height:

Without AspectRatio->Full, the original aspect ratio is preserved:

Using All for width or height causes that direction to stretch to the full size of the bar:

Use a different graphic for each side of the chart:

Use a different graphic for each row of data:

Styles are inherited from styles set through ChartStyle etc.:

Explicit styles set in the graphic will override other style settings:

The orientation of the pictorial graphic is unaffected by BarOrigin:

ChartLabels  (3)

By default, labels are placed on top of each bar pair:

Place group labels on each dataset:

Use Placed to control label placement:

ChartLayout  (1)

ChartLayout is overlapped by default:

Stacked layout:

ChartLegends  (2)

Generate a legend based on chart style:

Create legends for each dataset and bar pair:

ChartStyle  (3)

Use ChartStyle to style bars:

Give a list of styles:

Use "Gradient" colors from ColorData:

Use "Indexed" colors from ColorData:

Specify styles for each bar pair:

ColorFunction  (3)

Color by bar height:

Use ColorFunctionScaling->False to get unscaled height values:

ColorFunction overrides styles in ChartStyle:

Use ColorFunction to combine different style effects:

ColorFunctionScaling  (1)

By default, scaled height values are used:

Use ColorFunctionScaling->False to get unscaled height values:

ImageSize  (7)

Use named sizes such as Tiny, Small, Medium and Large:

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Setting AspectRatioFull will fill the available space:

Use maximum sizes for the width and height:

Use ImageSizeFull to fill the available space in an object:

Specify the image size as a fraction of the available space:

LabelingFunction  (5)

Use automatic labeling by values through Tooltip and StatusArea:

Do no labeling:

Use symbolic positions to control label placement:

Symbolic positions outside the bar:

Use the given chart labels as arguments to the labeling function:

Place complete labels in tooltips:

PerformanceGoal  (3)

Generate a paired bar chart with interactive highlighting:

Emphasize performance by disabling interactive behaviors:

Typically, less memory is required for non-interactive charts:

PlotTheme  (1)

Use a theme with simple ticks and grid lines in a high-contrast color scheme:

Change the color scheme:

Ticks  (4)

Ticks are placed automatically in each chart:

Use TicksNone to not draw any tick marks:

Place tick marks at specific positions:

Draw tick marks at the specified positions with the specified labels:

TicksStyle  (2)

Specify overall ticks style, including the tick labels:

Specify tick style for each of the axes:

Applications  (3)

Compare two different distributions:

Compare temperatures for two cities in 2009:

Compare two time slices for a random process:

Properties & Relations  (5)

PairedBarChart works on lists of heights:

Histogram and SmoothHistogram can be used to visualize single datasets:

Histogram3D and SmoothHistogram3D show bivariate data as surfaces:

DensityHistogram and SmoothDensityHistogram show bivariate data as density plots:

QuantilePlot and ProbabilityPlot compare distributions to each other:

BoxWhiskerChart and DistributionChart work with many datasets:

See Also

Histogram  PairedBarChart  SmoothHistogram  Histogram3D  QuantilePlot  ProbabilityPlot

Related Guides

    ▪
  • Statistical Visualization

History

Introduced in 2010 (8.0) | Updated in 2012 (9.0) ▪ 2014 (10.0) ▪ 2015 (10.2) ▪ 2025 (14.2)

Wolfram Research (2010), PairedHistogram, Wolfram Language function, https://reference.wolfram.com/language/ref/PairedHistogram.html (updated 2025).

Text

Wolfram Research (2010), PairedHistogram, Wolfram Language function, https://reference.wolfram.com/language/ref/PairedHistogram.html (updated 2025).

CMS

Wolfram Language. 2010. "PairedHistogram." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/PairedHistogram.html.

APA

Wolfram Language. (2010). PairedHistogram. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PairedHistogram.html

BibTeX

@misc{reference.wolfram_2025_pairedhistogram, author="Wolfram Research", title="{PairedHistogram}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/PairedHistogram.html}", note=[Accessed: 01-May-2026]}

BibLaTeX

@online{reference.wolfram_2025_pairedhistogram, organization={Wolfram Research}, title={PairedHistogram}, year={2025}, url={https://reference.wolfram.com/language/ref/PairedHistogram.html}, note=[Accessed: 01-May-2026]}

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