histogram

Histogram plot

• 

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

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.

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

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.

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.

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.

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

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.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | datetime | duration

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.

If you specify counts, then edges must be a row vector.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | datetime | duration

Categories — Categories included in histogram

cell array of character vectors | categorical array | string array | pattern scalar

Note

This option only applies to categorical histograms.

Categories included in histogram, specified as a cell array of character vectors, categorical array, string array, or pattern scalar.

• If you specify an input categorical array C, then by default, histogram plots a bar for each category in C. In that case, use Categories to specify a unique subset of the categories instead.

• If you specify bin counts, then Categories specifies the associated category names for the histogram.

Example: h = histogram(C,{'Large','Small'}) plots only the categorical data in the categories 'Large' and 'Small'.

Example: histogram(C,"Y" + wildcardPattern) plots data in the categories whose names begin with the letter Y.

Example: histogram('Categories',{'Yes','No','Maybe'},'BinCounts',[22 18 3]) plots a histogram that has three categories with the associated bin counts.

Example: h.Categories queries the categories that are in histogram object h.

Data Types: cell | categorical | string | pattern

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

BinWidth — Width of bins

positive scalar

Width of bins, specified as a positive scalar. If you specify BinWidth, then histogram can use a maximum of 65,536 bins (or 2¹⁶). If the specified bin width requires more bins, then histogram uses a larger bin width corresponding to the maximum number of bins.

• For datetime and duration data, BinWidth can be a scalar duration or calendar duration.

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

• This option does not apply to categorical data.

Example: histogram(X,'BinWidth',5) uses bins with a width of 5.

BinLimits — Bin limits

two-element vector

Bin limits, specified as a two-element vector, [bmin,bmax]. The first element indicates the first bin edge. The second element indicates the last bin edge.

This option computes using only the data that falls within the bin limits inclusively, X>=bmin & X<=bmax.

This option does not apply to categorical data.

Example: histogram(X,'BinLimits',[1,10]) bins only the values in X that are between 1 and 10 inclusive.

BinLimitsMode — Selection mode for bin limits

'auto' (default) | 'manual'

Selection mode for bin limits, specified as 'auto' or 'manual'. The default value is 'auto', so that the bin limits automatically adjust to the data.

• If you specify BinLimits or BinEdges, then BinLimitsMode is set to 'manual'. Specify BinLimitsMode as 'auto' to rescale the bin limits to the data.

• This option does not apply to histograms of categorical data.

BinMethod — Binning algorithm

'auto' (default) | 'scott' | 'fd' | 'integers' | 'sturges' | 'sqrt' | ...

Binning algorithm, specified as one of the values in this table.

Value	Description
'auto'	The default 'auto' algorithm chooses a bin width to cover the data range and reveal the shape of the underlying distribution.
'scott'	Scott’s rule is optimal if the data is close to being normally distributed. This rule is appropriate for most other distributions, as well. It uses a bin width of 3.5*std(X(:))*numel(X)^(-1/3).
'fd'	The Freedman-Diaconis rule is less sensitive to outliers in the data, and might be more suitable for data with heavy-tailed distributions. It uses a bin width of 2*iqr(X(:))*numel(X)^(-1/3), or when X contains extreme outliers, 0.2*(max(X(:))-min(X(:)))*numel(X)^(-1/3).
'integers'	The integer rule is useful with integer data, as it creates a bin for each integer. It uses a bin width of 1 and places bin edges halfway between integers. To avoid accidentally creating too many bins, you can use this rule to create a limit of 65536 bins (216). If the data range is greater than 65536, then the integer rule uses wider bins instead. 'integers' does not support datetime or duration data.
'sturges'	Sturges’ rule is popular due to its simplicity. It chooses the number of bins to be ceil(1 + log2(numel(X))) or 1, whichever is greater.
'sqrt'	The Square Root rule is widely used in other software packages. It chooses the number of bins to be ceil(sqrt(numel(X))) or 1, whichever is greater.

histogram adjusts the number of bins slightly so that the bin edges fall on "nice" numbers, rather than using these exact formulas.

For datetime or duration data, specify the binning algorithm as one of these units of time.

Value	Description	Data Type
"second"	Each bin is 1 second.	datetime and duration
"minute"	Each bin is 1 minute.	datetime and duration
"hour"	Each bin is 1 hour.	datetime and duration
"day"	Each bin is 1 calendar day. This value accounts for daylight saving time shifts.	datetime and duration
"week"	Each bin is 1 calendar week.	datetime only
"month"	Each bin is 1 calendar month.	datetime only
"quarter"	Each bin is 1 calendar quarter.	datetime only
"year"	Each bin is 1 calendar year. This value accounts for leap days.	datetime and duration
"decade"	Each bin is 1 decade (10 calendar years).	datetime only
"century"	Each bin is 1 century (100 calendar years).	datetime only

• If you specify BinMethod for datetime or duration data, then histogram can use a maximum of 65,536 bins (or 2¹⁶). If the specified bin duration requires more bins, then histogram uses a larger bin width corresponding to the maximum number of bins.

• If you specify BinLimits, NumBins, BinEdges, or BinWidth, then BinMethod is set to 'manual'.

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

• This option does not apply to categorical data.

Example: histogram(X,'BinMethod','integers') centers the bins on integers.

Categories

DisplayOrder — Category display order

'data' (default) | 'ascend' | 'descend'

Category display order, specified as 'data', 'ascend', or 'descend'.

• 'data' — Use the category order in the input data C.

• 'ascend' — Display the histogram with increasing bar heights.

• 'descend' — Display the histogram with decreasing bar heights.

This option only works with categorical data.

NumDisplayBins — Number of categories to display

scalar

Number of categories to display, specified as a scalar. You can change the ordering of categories displayed in the histogram using the 'DisplayOrder' option.

This option only works with categorical data.

ShowOthers — Toggle summary display of data belonging to undisplayed categories

'off' (default) | on/off logical value

Toggle summary display of data belonging to undisplayed categories, specified as 'on' or 'off', or as numeric or logical 1 (true) or 0 (false). A value of 'on' is equivalent to true, and 'off' is equivalent to false. Thus, you can use the value of this property as a logical value. The value is stored as an on/off logical value of type matlab.lang.OnOffSwitchState.

• Set this option to 'on' to display an additional bar in the histogram with the name 'Others'. This extra bar counts all elements that do not belong to categories displayed in the histogram.

• You can change the number of categories displayed in the histogram, as well as their order, using the 'NumDisplayBins' and 'DisplayOrder' options.

• This option only works with categorical data.

Data

Normalization — Type of normalization

'count' (default) | 'probability' | 'percentage' | 'countdensity' | 'cumcount' | 'pdf' | 'cdf'

Type of normalization, specified as one of the values in this table. For each bin i:

• $$v_i$$ is the bin value.

• $$c_i$$ is the number of elements in the bin.

• $$w_i$$ is the width of the bin.

• $$N$$ is the number of elements in the input data. This value can be greater than the binned data if the data contains missing values, such as NaN, or if some of the data lies outside the bin limits.

Value	Bin Values	Notes
'count' (default)	$$v_i=c_i$$	Count or frequency of observations. Sum of bin values is at most numel(X), or sum(ismember(X(:),'Categories')) for categorical data. The sum is less than this only when some of the input data is not included in the bins.
'probability'	$$v_i=\frac{c_i}{N}$$	Relative probability. The number of elements in each bin relative to the total number of elements in the input data is at most 1.
'percentage'	$$v_i=100*\frac{c_i}{N}$$	Relative percentage. The percentage of elements in each bin is at most 100.
'countdensity'	$$v_i=\frac{c_i}{w_i}$$	Count or frequency scaled by width of bin. For categorical data, this is the same as 'count'. 'countdensity' does not support datetime or duration data. The sum of the bin areas is at most numel(X).
'cumcount'	$$v_i={\displaystyle \sum _{j=1}^i{c}_j}$$	Cumulative count, or the number of observations in each bin and all previous bins. N(end) is at most numel(X), or sum(ismember(X(:),'Categories')) for categorical data.
'pdf'	$$v_i=\frac{c_i}{N\cdot w_i}$$	Probability density function estimate. For categorical data, this is the same as 'probability'. 'pdf' does not support datetime or duration data. The sum of the bin areas is at most 1.
'cdf'	$$v_i={\displaystyle \sum _{j=1}^i\frac{c_j}{N}}$$	Cumulative distribution function estimate. The count of each bin is equal to the cumulative relative number of observations in the bin and all previous bins. N(end) is at most 1.

Example: histogram(X,'Normalization','pdf') bins the data using an estimate of the probability density function.

Color and Styling

DisplayStyle — Histogram display style

'bar' (default) | 'stairs'

Histogram display style, specified as either 'bar' or 'stairs'.

• 'bar' — Display a histogram bar plot over each window of A. This method is useful for reducing periodic trends in data.

• 'stairs' — Display a stairstep plot, which displays the outline of the histogram without filling the interior.

Example: histogram(X,'DisplayStyle','stairs') plots the outline of the histogram.

Orientation — Orientation of bars

'vertical' (default) | 'horizontal'

Orientation of bars, specified as 'vertical' or 'horizontal'.

Example: histogram(X,'Orientation','horizontal') creates a histogram plot with horizontal bars.

BarWidth — Relative width of categorical bars

0.9 (default) | scalar in range [0,1]

Relative width of categorical bars, specified as a scalar value in the range [0,1]. Use this property to control the separation of categorical bars within the histogram. The default value is 0.9, which means that the bar width is 90% of the space from the previous bar to the next bar, with 5% of that space on each side.

If BarWidth is 1, then adjacent bars touch.

This option only works with categorical data.

Example: 0.5

FaceColor — Histogram bar color

'auto' (default) | 'none' | RGB triplet | hexadecimal color code | color name

Histogram bar color, specified as one of these values:

• 'none' — Bars are not filled.

• 'auto' — Histogram bar color is chosen automatically (default).

• RGB triplet, hexadecimal color code, or color name — Bars are filled with the specified color.

  RGB triplets and hexadecimal color codes are useful for specifying custom colors.

  • An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range [0,1]; for example, [0.4 0.6 0.7].

  • A hexadecimal color code is a character vector or a string scalar that starts with a hash symbol (#) followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Thus, the color codes "#FF8800", "#ff8800", "#F80", and "#f80" are equivalent.

  Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.

  Color Name	Short Name	RGB Triplet	Hexadecimal Color Code	Appearance
  "red"	"r"	[1 0 0]	"#FF0000"
  "green"	"g"	[0 1 0]	"#00FF00"
  "blue"	"b"	[0 0 1]	"#0000FF"
  "cyan"	"c"	[0 1 1]	"#00FFFF"
  "magenta"	"m"	[1 0 1]	"#FF00FF"
  "yellow"	"y"	[1 1 0]	"#FFFF00"
  "black"	"k"	[0 0 0]	"#000000"
  "white"	"w"	[1 1 1]	"#FFFFFF"

  This table lists the default color palettes for plots in the light and dark themes.

  Palette	Palette Colors
  "gem" — Light theme default Before R2025a: Most plots use these colors by default.
  "glow" — Dark theme default

  You can get the RGB triplets and hexadecimal color codes for these palettes using the orderedcolors and rgb2hex functions. For example, get the RGB triplets for the "gem" palette and convert them to hexadecimal color codes.

  RGB = orderedcolors("gem");
  H = rgb2hex(RGB);

  Before R2023b: Get the RGB triplets using RGB = get(groot,"FactoryAxesColorOrder").

  Before R2024a: Get the hexadecimal color codes using H = compose("#%02X%02X%02X",round(RGB*255)).

If you specify DisplayStyle as 'stairs', then histogram does not use the FaceColor property.

Example: histogram(X,'FaceColor','g') creates a histogram plot with green bars.

EdgeColor — Histogram edge color

'none' | 'auto' | RGB triplet | hexadecimal color code | color name

Histogram edge color, specified as one of these values:

• 'none' — Edges are not drawn.

• 'auto' — Color of each edge is chosen automatically.

• RGB triplet, hexadecimal color code, or color name — Edges use the specified color.

  RGB triplets and hexadecimal color codes are useful for specifying custom colors.

  • An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range [0,1]; for example, [0.4 0.6 0.7].

  • A hexadecimal color code is a character vector or a string scalar that starts with a hash symbol (#) followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Thus, the color codes "#FF8800", "#ff8800", "#F80", and "#f80" are equivalent.

  Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.

  Color Name	Short Name	RGB Triplet	Hexadecimal Color Code	Appearance
  "red"	"r"	[1 0 0]	"#FF0000"
  "green"	"g"	[0 1 0]	"#00FF00"
  "blue"	"b"	[0 0 1]	"#0000FF"
  "cyan"	"c"	[0 1 1]	"#00FFFF"
  "magenta"	"m"	[1 0 1]	"#FF00FF"
  "yellow"	"y"	[1 1 0]	"#FFFF00"
  "black"	"k"	[0 0 0]	"#000000"
  "white"	"w"	[1 1 1]	"#FFFFFF"

  This table lists the default color palettes for plots in the light and dark themes.

  Palette	Palette Colors
  "gem" — Light theme default Before R2025a: Most plots use these colors by default.
  "glow" — Dark theme default

  You can get the RGB triplets and hexadecimal color codes for these palettes using the orderedcolors and rgb2hex functions. For example, get the RGB triplets for the "gem" palette and convert them to hexadecimal color codes.

  RGB = orderedcolors("gem");
  H = rgb2hex(RGB);

  Before R2023b: Get the RGB triplets using RGB = get(groot,"FactoryAxesColorOrder").

  Before R2024a: Get the hexadecimal color codes using H = compose("#%02X%02X%02X",round(RGB*255)).

Example: histogram(X,'EdgeColor','r') creates a histogram plot with red bar edges.

FaceAlpha — Transparency of histogram bars

0.6 (default) | scalar value in range [0,1]

Transparency of histogram bars, specified as a scalar value in range [0,1]. histogram uses the same transparency for all the bars of the histogram. A value of 1 means fully opaque and 0 means completely transparent (invisible).

Example: histogram(X,'FaceAlpha',1) creates a histogram plot with fully opaque bars.

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.

LineStyle — Line style

"-" (default) | "--" | ":" | "-." | "none"

Line style, specified as one of the options listed in this table.

Line Style	Description	Resulting Line
"-"	Solid line
"--"	Dashed line
":"	Dotted line
"-."	Dash-dotted line
"none"	No line	No line

LineWidth — Width of bar outlines

0.5 (default) | positive value

Width of bar outlines, specified as a positive value in point units. One point equals 1/72 inch.

Example: 1.5

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

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

Histogram of Vector

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: [10000×1 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 … ] (1×38 double)
         BinWidth: 0.2000
        BinLimits: [-3.8000 3.6000]
    Normalization: 'count'
        FaceColor: 'auto'
        EdgeColor: [0.1294 0.1294 0.1294]

  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

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: [1000×1 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: [0.1294 0.1294 0.1294]

  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

Generate 1,000 random numbers and create a histogram.

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: [0.1294 0.1294 0.1294]

  Show all properties

Use the morebins function to coarsely adjust the number of bins.

Nbins = morebins(h);
Nbins = morebins(h)

Nbins = 
29

Adjust the bins at a fine grain level by explicitly setting the number of bins.

h.NumBins = 31;

Specify Bin Edges of Histogram

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

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 = 1×27 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: [0.1294 0.1294 0.1294]

  Show all properties

Histogram with Specified Normalization

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: [1000×1 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: [0.1294 0.1294 0.1294]

  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

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

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 on
h2 = 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;

Modify Histogram Properties

Create a histogram and return the Histogram object. Use the Histogram object to modify properties of the histogram after creating it.

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

h = 
  Histogram with properties:

             Data: [1000×1 double]
           Values: [2 2 15 15 33 47 62 90 100 114 121 107 93 85 43 37 17 9 5 1 2]
          NumBins: 21
         BinEdges: [-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 3.0000 3.3000]
         BinWidth: 0.3000
        BinLimits: [-3.0000 3.3000]
    Normalization: 'count'
        FaceColor: 'auto'
        EdgeColor: [0 0 0]

  Show all properties

Specify the edges of the bins with a vector.

h.BinEdges = [-3:3];

Normalize the bin counts so that the maximum bin count is 1.

h.BinCounts = h.BinCounts/max(h.BinCounts);

Label Bars with Bin Counts

You can label each rectangular bar of a histogram with the number of elements it represents.

Create a histogram.

x = randn(1000,1);
h = histogram(x,5);

Return the bin counts and the x-axis position of each bin center.

counts = h.Values;
binEdges = h.BinEdges;
binCenters = binEdges(1:end-1) + diff(binEdges)/2;

Add a label to each bar that displays the number of elements it represents.

text(binCenters,counts,num2str(counts'),HorizontalAlignment="center",VerticalAlignment="bottom")

Determine Underlying Probability Distribution

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 $$\mu$$, standard deviation $$\sigma$$, and variance $${\sigma }^2$$ is

$$f(x,\mu ,\sigma )=\frac{1}{\sigma \sqrt{2\pi }}\text{exp}[-\frac{(x-\mu {)}^2}{2{\sigma }^2}].$$

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

hold on
y = -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

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: [10×10 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: [0.1294 0.1294 0.1294]

  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 allowed options are:

  • 'BinWidth'

  • 'BinLimits'

  • 'Normalization'

  • 'DisplayStyle'

  • 'BinMethod' — The 'auto' and 'scott' bin methods are the same. The 'fd' bin method is not supported.

  • 'EdgeAlpha'

  • 'EdgeColor'

  • 'FaceAlpha'

  • 'FaceColor'

  • 'LineStyle'

  • 'LineWidth'

  • 'Orientation'

• Additionally, there is a cap on the maximum number of bars. The default maximum is 100.

• The morebins and fewerbins methods are not supported.

• Editing properties of the histogram object that require recomputing 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™.

The histogram function supports GPU array input with these 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

R2023b: Normalize using percentages

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