Histogram plot

expand all in page

Description

Histograms are a type of bar plot that group data into bins. After you create a Histogram object, you can modify aspects of the histogram by changing its property values. This is particularly useful for quickly modifying the properties of the bins or changing the display.

Creation

Syntax

histogram(X)

histogram(X,nbins)

histogram(X,edges)

histogram('BinEdges',edges,'BinCounts',counts)

histogram(C)

histogram(C,Categories)

histogram('Categories',Categories,'BinCounts',counts)

histogram(___,Name,Value)

histogram(ax,___)

h = histogram(___)

Description

example

histogram(X) creates a histogram plot of X. The histogram function uses an automatic binning algorithm that returns bins with a uniform width, chosen to cover the range of elements in X and reveal the underlying shape of the distribution. histogram displays the bins as rectangular bars such that the height of each rectangle indicates the number of elements in the bin.

example

histogram(X,nbins) specifies the number of bins.

example

histogram(X,edges) sorts X into bins with bin edges specified in a vector.

histogram('BinEdges',edges,'BinCounts',counts) plots the specified bin counts and does not do any data binning.

example

histogram(C) plots a histogram with a bar for each category in categorical array C.

histogram(C,Categories) plots only a subset of categories in C.

histogram('Categories',Categories,'BinCounts',counts) manually specifies categories and associated bin counts. histogram plots the specified bin counts and does not do any data binning.

example

histogram(___,Name,Value) specifies additional parameters using one or more name-value arguments for any of the previous syntaxes. For example, specify Normalization to use a different type of normalization. For a list of properties, see Histogram Properties.

histogram(ax,___) plots into the specified axes instead of into the current axes (gca). ax can precede any of the input argument combinations in the previous syntaxes.

example

h = histogram(___) returns a Histogram object. Use this to inspect and adjust the properties of the histogram. For a list of properties, see Histogram Properties.

Input Arguments

expand all

`X` — Data to distribute among bins
vector | matrix | multidimensional array

Data to distribute among bins, specified as a vector, matrix, or multidimensional array. histogram treats matrix and multidimensional array data as a single column vector, X(:), and plots a single histogram.

histogram ignores all NaN and NaT values. Similarly, histogram ignores Inf and -Inf values, unless the bin edges explicitly specify Inf or -Inf as a bin edge. Although NaN, NaT, Inf, and -Inf values are typically not plotted, they are still included in normalization calculations that include the total number of data elements, such as 'probability'.

Note

If X contains integers of type int64 or uint64 that are larger than flintmax, then it is recommended that you explicitly specify the histogram bin edges. histogram automatically bins the input data using double precision, which lacks integer precision for numbers greater than flintmax.

`C` — Categorical data
categorical array

Categorical data, specified as a categorical array. histogram does not plot undefined categorical values. However, undefined categorical values are still included in normalization calculations that include the total number of data elements, such as 'probability'.

Data Types: categorical

`nbins` — Number of bins
positive integer

Number of bins, specified as a positive integer. If you do not specify nbins, then histogram determines the number of bins from the values in X.

If you specify nbins with BinMethod, BinWidth or BinEdges, histogram only honors the last parameter.

Example: histogram(X,15) creates a histogram with 15 bins.

`edges` — Bin edges
vector

Bin edges, specified as a vector. edges(1) is the leading edge of the first bin, and edges(end) is the trailing edge of the last bin.

Each bin includes the leading edge, but does not include the trailing edge, except for the last bin which includes both edges.

For datetime and duration data, edges must be a datetime or duration vector in monotonically increasing order.

`counts` — Bin counts
vector

Bin counts, specified as a vector. Use this input to pass bin counts to histogram when the bin counts calculation is performed separately and you do not want histogram to do any data binning.

The size of counts must be equal to the number of bins.

For numeric histograms, the number of bins is length(edges)-1.
For categorical histograms, the number of bins is equal to the number of categories.

Example: histogram('BinEdges',-2:2,'BinCounts',[5 8 15 9])

Example: histogram('Categories',{'Yes','No','Maybe'},'BinCounts',[22 18 3])

`ax` — Target axes
`Axes` object | `PolarAxes` object

Target axes, specified as an Axes object or a PolarAxes object. If you do not specify the axes and if the current axes are Cartesian axes, then the histogram function uses the current axes (gca). To plot into polar axes, specify the PolarAxes object as the first input argument or use the polarhistogram function.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: histogram(X,BinWidth=5)

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: histogram(X,'BinWidth',5)

Note

The properties listed here are only a subset. For a complete list, see Histogram Properties.

Bins

expand all

`EdgeAlpha` — Transparency of histogram bar edges
`1` (default) | scalar in range `[0,1]`

Transparency of histogram bar edges, specified as a scalar value in the range [0,1]. A value of 1 means fully opaque and 0 means completely transparent (invisible).

Example: histogram(X,'EdgeAlpha',0.5) creates a histogram plot with semi-transparent bar edges.

Output Arguments

expand all

`h` — Histogram
object

Histogram, returned as an object. For more information, see Histogram Properties.

Properties

Histogram Properties

Histogram appearance and behavior

Object Functions

morebins	Increase number of histogram bins
fewerbins	Decrease number of histogram bins

Examples

collapse all

Histogram of Vector

Open Live Script

Generate 10,000 random numbers and create a histogram. The histogram function automatically chooses an appropriate number of bins to cover the range of values in x and show the shape of the underlying distribution.

x = randn(10000,1);h = histogram(x)

h = Histogram with properties: Data: [10000x1 double] Values: [2 2 1 6 7 17 29 57 86 133 193 271 331 421 540 613 730 748 776 806 824 721 623 503 446 326 234 191 132 78 65 33 26 11 8 5 5] NumBins: 37 BinEdges: [-3.8000 -3.6000 -3.4000 -3.2000 -3 -2.8000 -2.6000 -2.4000 -2.2000 -2 -1.8000 -1.6000 -1.4000 -1.2000 -1 -0.8000 -0.6000 -0.4000 -0.2000 0 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000 2.2000 ... ] (1x38 double) BinWidth: 0.2000 BinLimits: [-3.8000 3.6000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0 0 0] Use GET to show all properties

When you specify an output argument to the histogram function, it returns a histogram object. You can use this object to inspect the properties of the histogram, such as the number of bins or the width of the bins.

Find the number of histogram bins.

nbins = h.NumBins

nbins = 37

Specify Number of Histogram Bins

Open Live Script

Plot a histogram of 1,000 random numbers sorted into 25 equally spaced bins.

x = randn(1000,1);nbins = 25;h = histogram(x,nbins)

h = Histogram with properties: Data: [1000x1 double] Values: [1 3 0 6 14 19 31 54 74 80 92 122 104 115 88 80 38 32 21 9 5 5 5 0 2] NumBins: 25 BinEdges: [-3.4000 -3.1200 -2.8400 -2.5600 -2.2800 -2 -1.7200 -1.4400 -1.1600 -0.8800 -0.6000 -0.3200 -0.0400 0.2400 0.5200 0.8000 1.0800 1.3600 1.6400 1.9200 2.2000 2.4800 2.7600 3.0400 3.3200 3.6000] BinWidth: 0.2800 BinLimits: [-3.4000 3.6000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0 0 0] Use GET to show all properties

Find the bin counts.

counts = h.Values

counts = 1×25 1 3 0 6 14 19 31 54 74 80 92 122 104 115 88 80 38 32 21 9 5 5 5 0 2

Change Number of Histogram Bins

Open Live Script

Generate 1,000 random numbers and create a histogram.

Specify Bin Edges of Histogram

Open Live Script

Generate 1,000 random numbers and create a histogram. Specify the bin edges as a vector with wide bins on the edges of the histogram to capture the outliers that do not satisfy $| x | < 2$ . The first vector element is the left edge of the first bin, and the last vector element is the right edge of the last bin.

x = randn(1000,1);edges = [-10 -2:0.25:2 10];h = histogram(x,edges);

Specify the Normalization property as 'countdensity' to flatten out the bins containing the outliers. Now, the area of each bin (rather than the height) represents the frequency of observations in that interval.

h.Normalization = 'countdensity';

Plot Categorical Histogram

Open Live Script

Create a categorical vector that represents votes. The categories in the vector are 'yes', 'no', or 'undecided'.

A = [0 0 1 1 1 0 0 0 0 NaN NaN 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1];C = categorical(A,[1 0 NaN],{'yes','no','undecided'})

C = 1x27 categorical no no yes yes yes no no no no undecided undecided yes no no no yes no yes no yes no no no yes yes yes yes

Plot a categorical histogram of the votes, using a relative bar width of 0.5.

h = histogram(C,'BarWidth',0.5)

h = Histogram with properties: Data: [no no yes yes yes no no no no undecided undecided yes no no no yes no yes no yes no no no yes yes yes yes] Values: [11 14 2] NumDisplayBins: 3 Categories: {'yes' 'no' 'undecided'} DisplayOrder: 'data' Normalization: 'count' DisplayStyle: 'bar' FaceColor: 'auto' EdgeColor: [0 0 0] Use GET to show all properties

Histogram with Specified Normalization

Open Live Script

Generate 1,000 random numbers and create a histogram using the 'probability' normalization.

x = randn(1000,1);h = histogram(x,'Normalization','probability')

h = Histogram with properties: Data: [1000x1 double] Values: [0.0030 1.0000e-03 0.0020 0.0150 0.0170 0.0270 0.0530 0.0790 0.0850 0.1010 0.1270 0.1100 0.1240 0.0950 0.0670 0.0320 0.0270 0.0160 0.0060 0.0060 0.0040 1.0000e-03 0.0020] NumBins: 23 BinEdges: [-3.3000 -3.0000 -2.7000 -2.4000 -2.1000 -1.8000 -1.5000 -1.2000 -0.9000 -0.6000 -0.3000 0 0.3000 0.6000 0.9000 1.2000 1.5000 1.8000 2.1000 2.4000 2.7000 3 3.3000 3.6000] BinWidth: 0.3000 BinLimits: [-3.3000 3.6000] Normalization: 'probability' FaceColor: 'auto' EdgeColor: [0 0 0] Use GET to show all properties

Compute the sum of the bar heights. With this normalization, the height of each bar is equal to the probability of selecting an observation within that bin interval, and the height of all of the bars sums to 1.

S = sum(h.Values)

S = 1

Histogram Using Percentages

Open Live Script

Generate 100,000 normally distributed random numbers. Use a standard deviation of 15 and a mean of 100.

x = 100 + 15*randn(1e5,1);

Plot a histogram of the random numbers. Scale and label the y-axis as percentages.

edges = 55:15:145;histogram(x,edges,Normalization="percentage")ytickformat("percentage")

Plot Multiple Histograms

Open Live Script

Generate two vectors of random numbers and plot a histogram for each vector in the same figure.

x = randn(2000,1);y = 1 + randn(5000,1);h1 = histogram(x);hold onh2 = histogram(y);

Since the sample size and bin width of the histograms are different, it is difficult to compare them. Normalize the histograms so that all of the bar heights add to 1, and use a uniform bin width.

h1.Normalization = 'probability';h1.BinWidth = 0.25;h2.Normalization = 'probability';h2.BinWidth = 0.25;

Adjust Histogram Properties

Open Live Script

Generate 1,000 random numbers and create a histogram. Return the histogram object to adjust the properties of the histogram without recreating the entire plot.

x = randn(1000,1);h = histogram(x)

h = Histogram with properties: Data: [1000×1 double] Values: [3 1 2 15 17 27 53 79 85 101 127 110 124 95 67 32 27 16 6 6 4 1 2] NumBins: 23 BinEdges: [-3.3000 -3.0000 -2.7000 -2.4000 -2.1000 -1.8000 -1.5000 -1.2000 -0.9000 -0.6000 -0.3000 0 0.3000 0.6000 0.9000 1.2000 1.5000 1.8000 2.1000 2.4000 2.7000 3 3.3000 3.6000] BinWidth: 0.3000 BinLimits: [-3.3000 3.6000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0 0 0] Show all properties

Specify exactly how many bins to use.

h.NumBins = 15;

Specify the edges of the bins with a vector. The first value in the vector is the left edge of the first bin. The last value is the right edge of the last bin.

h.BinEdges = [-3:3];

Change the color of the histogram bars.

h.FaceColor = [0 0.5 0.5];h.EdgeColor = 'r';

Determine Underlying Probability Distribution

Open Live Script

Generate 5,000 normally distributed random numbers with a mean of 5 and a standard deviation of 2. Plot a histogram with Normalization set to 'pdf' to produce an estimation of the probability density function.

x = 2*randn(5000,1) + 5;histogram(x,'Normalization','pdf')

In this example, the underlying distribution for the normally distributed data is known. You can, however, use the 'pdf' histogram plot to determine the underlying probability distribution of the data by comparing it against a known probability density function.

The probability density function for a normal distribution with mean $μ$ , standard deviation $σ$ , and variance $σ^{2}$ is

$f (x, μ, σ) = \frac{1}{σ \sqrt{2 π}} exp [- \frac{(x - μ)^{2}}{2 σ^{2}}] .$

Overlay a plot of the probability density function for a normal distribution with a mean of 5 and a standard deviation of 2.

hold ony = -5:0.1:15;mu = 5;sigma = 2;f = exp(-(y-mu).^2./(2*sigma^2))./(sigma*sqrt(2*pi));plot(y,f,'LineWidth',1.5)

Saving and Loading Histogram Objects

Open Live Script

Use the savefig function to save a histogram figure.

histogram(randn(10));savefig('histogram.fig');close gcf

Use openfig to load the histogram figure back into MATLAB®. openfig also returns a handle to the figure, h.

h = openfig('histogram.fig');

Use the findobj function to locate the correct object handle from the figure handle. This allows you to continue manipulating the original histogram object used to generate the figure.

y = findobj(h,'type','histogram')

y = Histogram with properties: Data: [10x10 double] Values: [2 17 28 32 16 3 2] NumBins: 7 BinEdges: [-3 -2 -1 0 1 2 3 4] BinWidth: 1 BinLimits: [-3 4] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0 0 0] Use GET to show all properties

Tips

Histogram plots created using histogram have a context menu in plot edit mode that enables interactive manipulations in the figure window. For example, you can use the context menu to interactively change the number of bins, align multiple histograms, or change the display order.
When you add data tips to a histogram plot, they display the bin edges and bin count.

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

This function supports tall arrays with the limitations:

Some input options are not supported. The allowedoptions are:
- 'BinWidth'
- 'BinLimits'
- 'Normalization'
- 'DisplayStyle'
- 'BinMethod' — The 'auto' and 'scott' binmethods are the same. The 'fd' bin method is notsupported.
- 'EdgeAlpha'
- 'EdgeColor'
- 'FaceAlpha'
- 'FaceColor'
- 'LineStyle'
- 'LineWidth'
- 'Orientation'
Additionally, there is a cap on the maximum numberof bars. The default maximum is 100.
The morebins and fewerbins methodsare not supported.
Editing properties of the histogram object that requirerecomputing the bins is not supported.

For more information, see Tall Arrays for Out-of-Memory Data.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

This function accepts GPU arrays, but does not run on a GPU.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Usage notes and limitations:

This function operates on distributed arrays, but executes in the client MATLAB.

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced in R2014b

expand all

R2023b: Normalize using percentages

You can create histograms with percentages on the vertical axis by setting the Normalization name-value argument to 'percentage'.

MATLAB Command

You clicked a link that corresponds to this MATLAB command:

Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.

Select a Web Site

Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .

You can also select a web site from the following list:

Americas

América Latina (Español)
Canada (English)
United States (English)

Europe

Belgium (English)
Denmark (English)
Deutschland (Deutsch)
España (Español)
Finland (English)
France (Français)
Ireland (English)
Italia (Italiano)
Luxembourg (English)

Netherlands (English)
Norway (English)
Österreich (Deutsch)
Portugal (English)
Sweden (English)
Switzerland
- Deutsch
- English
- Français
United Kingdom (English)

Asia Pacific

Australia (English)
India (English)
New Zealand (English)
中国
- 简体中文
- English
日本 (日本語)
한국 (한국어)

Contact your local office

Histogram plot - MATLAB (2024)

Description

Creation

Syntax

Description

Input Arguments

X — Data to distribute among binsvector | matrix | multidimensional array

C — Categorical data categorical array

nbins — Number of bins positive integer

edges — Bin edges vector

counts — Bin counts vector

ax — Target axes Axes object | PolarAxes object

EdgeAlpha — Transparency of histogram bar edges 1 (default) | scalar in range [0,1]

Output Arguments

h — Histogramobject

Properties

Object Functions

Examples

Histogram of Vector

Specify Number of Histogram Bins

Change Number of Histogram Bins

Specify Bin Edges of Histogram

Plot Categorical Histogram

Histogram with Specified Normalization

Histogram Using Percentages

Plot Multiple Histograms

Adjust Histogram Properties

Determine Underlying Probability Distribution

Saving and Loading Histogram Objects

Tips

Extended Capabilities

Tall Arrays Calculate with arrays that have more rows than fit in memory.

GPU Arrays Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed ArraysPartition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Version History

R2023b: Normalize using percentages

See Also

Topics

MATLAB Command

Americas

Europe

Asia Pacific

`X` — Data to distribute among bins
vector | matrix | multidimensional array

`C` — Categorical data
categorical array

`nbins` — Number of bins
positive integer

`edges` — Bin edges
vector

`counts` — Bin counts
vector

`ax` — Target axes
`Axes` object | `PolarAxes` object

`EdgeAlpha` — Transparency of histogram bar edges
`1` (default) | scalar in range `[0,1]`

`h` — Histogram
object

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.