BUILT-IN MATHEMATICA SYMBOL

Histogram

plots a histogram of the values

.

Histogram

plots a histogram with bin width specification bspec.

Histogram

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

Histogram

plots histograms for multiple datasets

.

MORE INFORMATION

Histogram[data] by default plots a histogram with equal bin widths chosen to approximate an assumed underlying smooth distribution of the values .

The following bin width specifications bspec can be given:

	n	use n bins
	{dx}	use bins of width dx
	{x_min,x_max,dx}	use bins of width dx from to
	{{b₁,b₂,...}}	use the bins
	Automatic	determine bin widths automatically
	"name"	use a named binning method
	{"Log",bspec}	apply binning bspec on log-transformed data
	fb	apply fb to get an explicit bin specification

The binning specification 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 is applied to a list of all , and should return an explicit bin list .

Different forms of histogram can be obtained by giving different bin height specifications hspec in Histogram. The following forms can be used:

	"Count"	the number of values lying in each bin
	"CumulativeCount"	cumulative counts
	"SurvivalCount"	survival counts
	"Probability"	fraction of values lying in each bin
	"PDF"	probability density function
	"CDF"	cumulative distribution function
	"SF"	survival function
	"HF"	hazard function
	"CHF"	cumulative hazard function
	{"Log",hspec}	log-transformed height specification
	fh	heights obtained by applying fh to bins and counts

The function fh in Histogram is applied to two arguments: a list of bins , and corresponding list of counts . The function should return a list of heights to be used for each of the .

Only values that are real numbers are assigned to bins; others are taken to be missing.

In Histogram, automatic bin locations are determined by combining all the datasets .

Histogram renders the histogram elements associated with dataset according to the specification defined by the symbolic wrapper .

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:

AspectRatio	1/GoldenRatio	overall ratio of width to height
Axes	True	whether to draw axes
BarOrigin	Bottom	origin of histogram bars
ChartBaseStyle	Automatic	overall style for bars
ChartElementFunction	Automatic	how to generate raw graphics for bars
ChartElements	Automatic	graphics to use in each of the bars
ChartLabels	None	category labels for datasets
ChartLayout	Automatic	overall layout to use
ChartStyle	Automatic	style for bars
ChartLegends	None	legends for data elements and datasets
ColorFunction	Automatic	how to color bars
ColorFunctionScaling	True	whether to normalize arguments to ColorFunction
LabelingFunction	Automatic	how to label elements
LegendAppearance	Automatic	overall appearance of legends
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
ScalingFunctions	None	how to scale individual coordinates

Possible settings for ChartLayout include and .

The arguments supplied to ChartElementFunction are the bin region , the bin values lists, and metadata from each level in a nested list of datasets.

A list of built-in settings for ChartElementFunction can be obtained from .

The argument supplied to ColorFunction is the height for each bin.

With ScalingFunctions, the coordinate is scaled using 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

CLOSE ALL

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:

Generate a histogram for a list of values:

In[1]:=

Out[1]=

Multiple datasets:

In[1]:=

In[2]:=

Out[2]=

Generate a probability histogram for a list of values:

In[1]:=

Out[1]=

Pictorial bars:

In[1]:=

Out[1]=

Use procedural bars:

In[2]:=

Out[2]=

Scope (21)

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:

Nonreal data is taken to be missing:

Use different layouts to display multiple datasets:

Control the origin of bars:

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:

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 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 (50)

Change the bar origin:

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:

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:

Get a list of built-in settings for ChartElementFunction:

For detailed settings use Palettes ► ChartElementSchemes:

ChartElementFunction appropriate to show the global scale:

Write a custom ChartElementFunction:

Built-in element function may have options; use Palettes ► ChartElementSchemes to set them:

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:

Use different layouts to display multiple datasets:

With multiple datasets that are fairly disjoint typically

works better:

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:

Use ChartStyle to style bars:

Give a list of styles:

Use

colors from ColorData:

Use

colors from ColorData:

Styles are used cyclically:

Style overrides settings for ChartStyle:

ColorFunction overrides settings for ChartStyle:

ChartElements may override settings for ChartStyle:

Color by bar height:

Use ColorFunctionScaling->False to get unscaled height values:

ColorFunction overrides styles in ChartStyle:

Use ColorFunction to combine different style effects:

By default scaled height values are used:

Use ColorFunctionScaling->False, to get unscaled height values:

Use automatic labeling by values through Tooltip and StatusArea:

Do no labeling:

Use Placed 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:

Generate a bar chart with interactive highlighting:

Emphasize performance by disabling interactive behaviors:

Typically less memory is required for noninteractive charts:

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:

Applications (13)

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 Mathematica:

Distribution of lengths of human chromosomes:

Create a ListLinePlot using counts extracted from a histogram:

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

Click on 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 Thue-Morse nested sequence

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:

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 parametric probability density function:

Show together with Histogram of random data:

Neat Examples (1)

Overlay several PDF plots for Poisson distributions: