Built-in Mathematica Symbol

Histogram

Histogram[{x₁, x₂, ...}]
plots a histogram of the values x_i.

Histogram[{x₁, x₂, ...}, w]
plots a histogram with bin width specification w.

Histogram[{x₁, x₂, ...}, w, hspec]
plots a histogram with bin heights computed according to the specification hspec.

Histogram[{data₁, data₂, ...}, ...]
plots histograms for multiple datasets data_i.

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

	n	use n bins
	{dx}	use bins of width dx
	{x_min,x_max,dx}	use bins of width dx from x_min to x_max
	{{b₁,b₂,...}}	use the bins [b₁, b₂), [b₂, b₃), ...
	Automatic	determine bin widths automatically
	"name"	use a named binning method
	fw	apply fw to get an explicit bin specification {b₁, b₂, ...}

	"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
	"Wand"	one-level recursive approximate Wand binning
	"Log"	logarithmic bin widths

The function fw in Histogram[data, fw] is applied to a list of all x_i, 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, w, hspec]. The following forms can be used:

	"Count"	the number of values lying in each bin
	"Probability"	fraction of values lying in each bin
	"ProbabilityDensity"	fraction of values divided by bin width
	"LogCount", "LogProbability", "LogProbabilityDensity"	logarithmic heights
	fh	heights obtained by applying fh to bins and counts

The function fh in Histogram[data, w, 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 c_i.

Only values x_i 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 data_i.

Histogram[{..., w_i[data_i, ...], ...}, ...] renders the histogram elements associated with dataset data_i according to the specification defined by the symbolic wrapper w_i.

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

The arguments supplied to ChartElementFunction are the bin region {{x_min, x_max}, {y_min, y_max}}, 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"].

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.