Histogram

Histogram[{x1,x2,}]

plots a histogram of the values xi.

Histogram[{x1,x2,},bspec]

plots a histogram with bin width specification bspec.

Histogram[{x1,x2,},bspec,hspec]

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

Histogram[{data1,data2,},]

plots histograms for multiple datasets datai.

Details and Options

  • Histogram[data] by default plots a histogram with equal bin widths chosen to approximate an assumed underlying smooth distribution of the values xi.
  • Data values xi can be given in the following forms:
  • xia number
    Quantity[xi,unit]a number with a unit
  • Datasets datai have the following forms and interpretations:
  • {x1,x2,}a list of values xi
    <|k1x1,k2x2,|>the values xi from the association
    QuantityArraythe magnitudes
    TimeSeries,EventSeries,the values from time series data
    WeightedDatathe count for each value is its weight
    w[datai]wrapper w for dataset datai
  • 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 Histogram[data,fb] is applied to a list of all xi, and should return an explicit bin list {b1,b2,}.
  • Different forms of histogram can be obtained by giving different bin height specifications hspec in Histogram[data,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 Histogram[data,bspec,fh] is applied to two arguments: a list of bins {{b1,b2},{b2,b3},}, and a 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 Histogram[{data1,data2,},], automatic bin locations are determined by combining all the datasets datai.
  • Histogram[{,wi[datai,],},] renders the histogram elements associated with dataset datai according to the specification defined by the symbolic wrapper wi.
  • Possible symbolic wrappers are the same as for BarChart, and include Style, Labeled, Legended, etc.
  • Histogram has the same options as Graphics with the following additions and changes:
  • AspectRatio1/GoldenRatiooverall ratio of width to height
    AxesTruewhether to draw axes
    BarOriginBottomorigin of histogram bars
    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
    LabelingFunctionAutomatichow 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
  • Possible settings for ChartLayout include "Overlapped" and "Stacked".
  • 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["Histogram"].
  • The argument supplied to ColorFunction is the height for each bin.
  • With ScalingFunctions->{sx,sy}, the 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.

Examples

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Basic Examples  (4)

Generate a histogram for a list of values:

Multiple datasets:

Generate a probability histogram for a list of values:

Pictorial bars:

Use procedural bars:

Scope  (31)

Data and Layouts  (18)

Specify the number of bins to use:

Specify the bin width:

The bin delimiters:

The bin delimiters as an explicit list:

Bins for discrete values are centered over the values when possible:

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:

Nonreal data is taken to be missing:

The data may include units:

Specify units to use:

Specify binning spec with units:

The values in an association are used as elements:

Associations can be nested:

Use the keys as labels:

Use the keys as legends:

The time stamps in TimeSeries, EventSeries, and TemporalData are ignored:

Weights in WeightedData affect the shape of histogram:

The censoring and truncation information in EventData also affects the histogram:

Use different layouts to display multiple datasets:

Control the origin of bars:

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:

Style can be used to override styles:

Use any graphic for pictorial bars:

Use built-in, programmatically generated bars:

For detailed settings, use Palettes ChartElementSchemes:

Use a monochrome theme:

Labeling and Legending  (7)

Use Labeled to add a label to a dataset:

Use symbolic positions for label placement:

Provide value labels for bars by using LabelingFunction:

Use Placed to control placement and formatting:

Add categorical legend entries for datasets:

Use Legended to add additional legend entries:

Use Placed to affect the positioning of legends:

Options  (52)

BarOrigin  (1)

Change the bar origin:

ChartBaseStyle  (4)

Use ChartBaseStyle to style bars:

ChartBaseStyle combines with ChartStyle:

ChartStyle may override settings for ChartBaseStyle:

ChartBaseStyle combines with Style:

Style may override settings for ChartBaseStyle:

ChartBaseStyle combines with ColorFunction:

ColorFunction may override settings for ChartBaseStyle:

ChartElementFunction  (4)

Get a list of built-in settings for ChartElementFunction:

For detailed settings, use Palettes ChartElementSchemes:

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  (9)

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:

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

Use a different graphic for each row of data:

Graphics are used cyclically:

Styles are inherited from styles set through ChartStyle etc:

Style can override the settings from ChartStyle:

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

Create true 3D-shaded bars:

ChartLabels  (6)

Place dataset labels above each histogram:

Labeled wrappers around datasets will place additional labels:

Use Placed to control label placement:

Symbolic positions outside the bar:

Coordinate-based placement relative to a histogram:

Place all labels at the lower-left corner and vary the coordinates within the label:

Use the third argument to Placed to control formatting:

Use a named formatting function:

Use a hyperlink label:

Place multiple labels:

ChartLayout  (2)

Use different layouts to display multiple datasets:

With multiple datasets that are fairly disjoint, typically "Overlapped" works better:

ChartLegends  (2)

Generate a legend based on chart style:

Use Legended to add additional legend entries:

Use Legended to specify individual legend entries:

Use Placed to control the placement of legends:

ChartStyle  (5)

Use ChartStyle to style bars:

Give a list of styles:

Use "Gradient" colors from ColorData:

Use "Indexed" colors from ColorData:

Styles are used cyclically:

Style overrides settings for ChartStyle:

ColorFunction overrides settings for ChartStyle:

ChartElements may override settings for ChartStyle:

ColorFunction  (4)

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  (2)

By default, scaled height values are used:

Use ColorFunctionScaling->False to get unscaled height values:

LabelingFunction  (7)

Use automatic labeling by values through Tooltip and StatusArea:

Do no labeling:

Use symbolic positions to control label placement:

Coordinate-based placement relative to a bar:

Control the formatting of labels:

Use the dataset position index to generate the label:

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

PerformanceGoal  (1)

Generate a bar chart with interactive highlighting:

Emphasize performance by disabling interactive behaviors:

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

PlotRangePadding  (3)

Specify a single plot range padding for all directions:

Specify a separate plot range padding for horizontal and vertical directions:

Specify a separate plot range padding for each direction:

PlotTheme  (2)

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

Change the color scheme:

Applications  (14)

Overlay a plot of the PDF for a normal distribution:

Number of elements discovered each decade from 1700 to 2000:

Create a histogram of reference page sizes in the Wolfram System:

Distribution of lengths of human chromosomes:

Create a ListLinePlot using counts extracted from a histogram:

Click a dataset in the histogram to hear an acoustic representation of the counts:

Click the bars to hear the counts in the corresponding bin:

Create a matrix of handwritten digits using Graphics Drawing Tools:

Compute the histogram of line angles used in a character drawing:

Create histograms for each digit showing the frequency of line angles:

Create a stacked histogram of male and female life expectancy for all countries:

Select a subset of languages available in DictionaryLookup:

Mouse over the bars to get the word counts with a particular string length:

Power spectrum of the ThueMorse nested sequence [more info]:

Distribution of frequencies:

Create a cumulative histogram:

Create a stacked cumulative histogram:

Wind direction from WeatherData ranges from 0° to 360°:

Get wind direction data for Willard Airport (CMI) at Champaign, Illinois:

Define a chart element function that stores bin width and count data using Sow:

Create a histogram of the wind directions, and store the bin width and frequencies:

Create a polar histogram of the wind-direction frequencies:

Histogram for the slice distribution of a random process:

Histogram for several slices of a process:

Properties & Relations  (3)

Histogram automatically determines bins to use based on data:

Use BinCounts for explicit binning of data:

Display using BarChart:

Use PDF to get a parametric probability density function:

Show together with Histogram of random data:

Possible Issues  (2)

Discrete values that don't align with the bin width can result in gaps:

Bins include the left endpoint but not the right, which can result in unexpected bins:

The value 1 is not included in this histogram because it would be in the bin [1,1.2):

Neat Examples  (1)

Overlay several PDF plots for Poisson distributions:

Introduced in 2008
 (7.0)
 |
Updated in 2010
 (8.0)
2012
 (9.0)
2014
 (10.0)
2015
 (10.2)