histogram
Histogram plot
Description
Histograms are a type of bar plot for numeric data that group the 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
Description
histogram(
creates a histogram
plot of X
)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 rectangles such that the height of each rectangle
indicates the number of elements in the bin.
histogram(
, where
C
)C
is a categorical array, plots a histogram with a
bar for each category in C
.
histogram(
plots only the subset of categories specified by
C
,Categories
)Categories
.
histogram('Categories',
manually specifies categories and associated bin counts.
Categories
,'BinCounts',counts
)histogram
plots the specified bin counts and does
not do any data binning.
histogram(___,
specifies additional options with one or more Name,Value
)Name,Value
pair arguments using any of the previous syntaxes. For example, you can
specify 'BinWidth'
and a scalar to adjust the width of
the bins, or 'Normalization'
with a valid option
('count'
, 'probability'
,
'countdensity'
, 'pdf'
,
'cumcount'
, or 'cdf'
) to use a
different type of normalization. For a list of properties, see Histogram Properties.
histogram(
plots into the axes specified by ax
,___)ax
instead of into the
current axes (gca
). The option ax
can
precede any of the input argument combinations in the previous
syntaxes.
returns a h
= histogram(___)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. If X
is not a vector, then
histogram
treats it 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
automatically calculates how many bins to use based on the values in
X
.
Example: histogram(X,15)
creates a histogram with 15
bins.
edges
— Bin edges
vector
Bin edges, specified as a vector. edges(1)
is the
left edge of the first bin, and edges(end)
is the
right edge of the last bin.
The value X(i)
is in the k
th bin
if edges(k)
≤ X(i)
<
edges(k+1)
. The last bin also includes the right
bin edge, so that it contains X(i)
if
edges(end1)
≤ X(i)
≤
edges(end)
.
For datetime and duration data, edges
must be a
datetime or duration vector in monotonically increasing order.
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 inC
. In that case, useCategories
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 length 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.
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: histogram(X,'BinWidth',5)
The histogram properties listed here are only a subset. For a complete list, see Histogram Properties.
BarWidth
— Relative width of categorical bars
0.9
(default)  scalar in range [0,1]
Note
This option only applies to histograms of categorical data.
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 you set this property to 1
, then adjacent
bars touch.
Example: 0.5
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
BinLimits
— Bin limits
twoelement vector
Bin limits, specified as a twoelement vector, [bmin,bmax]
.
This option plots a histogram using the values in the input array, X
,
that fall between bmin
and bmax
inclusive.
That is, X(X>=bmin & X<=bmax)
.
This option does not apply to histograms of categorical data.
Example: histogram(X,'BinLimits',[1,10])
plots
a histogram using 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 explicitly specify either BinLimits
or BinEdges
,
then BinLimitsMode
is automatically set to 'manual'
.
In that case, 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 


The default 

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


The FreedmanDiaconis rule is less sensitive
to outliers in the data, and might be more
suitable for data with heavytailed distributions.
It uses a bin width of


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 (2^{16}). If the data range is greater than 65536, then the integer rule uses wider bins instead. Note


Sturges’ rule is popular due to its
simplicity. It chooses the number of bins to be


The Square Root rule is widely used in other
software packages. It chooses the number of bins
to be

histogram
does not always choose the number of bins using these exact
formulas. Sometimes the number of bins is adjusted slightly so that the bin edges fall on
"nice" numbers.
For datetime data, the bin method can be one of these units of time:
'second'  'month' 
'minute'  'quarter' 
'hour'  'year' 
'day'  'decade' 
'week'  'century' 
For duration data, the bin method can be one of these units of time:
'second'  'day' 
'minute'  'year' 
'hour' 
If you specify BinMethod
with datetime or duration data, then
histogram
can use a maximum of 65,536 bins (or
2^{16}). If the specified bin duration requires more bins,
then histogram
uses a larger bin width corresponding to the maximum
number of bins.
This option does not apply to histograms of categorical data.
Note
If you set the BinLimits
, NumBins
, BinEdges
,
or BinWidth
property, then the BinMethod
property
is set to 'manual'
.
Example: histogram(X,'BinMethod','integers')
creates
a histogram with the bins centered on integers.
BinWidth
— Width of bins
scalar
Width of bins, specified as a scalar. When you specify BinWidth
,
then histogram
can use a maximum of 65,536 bins
(or 2^{16}).
If instead 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, the value of 'BinWidth'
can
be a scalar duration or calendar duration.
This option does not apply to histograms of categorical data.
Example: histogram(X,'BinWidth',5)
uses bins
with a width of 5.
DisplayOrder
— Category display order
'data'
(default)  'ascend'
 'descend'
Category display order, specified as 'ascend'
, 'descend'
,
or 'data'
. With 'ascend'
or 'descend'
,
the histogram displays with increasing or decreasing bar heights.
The default 'data'
value uses the category order
in the input data, C
.
This option only works with categorical data.
DisplayStyle
— Histogram display style
'bar'
(default)  'stairs'
Histogram display style, specified as either 'bar'
or 'stairs'
.
Specify 'stairs'
to display a stairstep plot, which
displays the outline of the histogram without filling the interior.
The default value of 'bar'
displays a histogram
bar plot.
Example: histogram(X,'DisplayStyle','stairs')
plots
the outline of the histogram.
EdgeAlpha
— Transparency of histogram bar edges
1
(default)  scalar value between 0
and
1
inclusive
Transparency of histogram bar edges, specified as a scalar value
between 0
and 1
inclusive. A
value of 1
means fully opaque and
0
means completely transparent
(invisible).
Example: histogram(X,'EdgeAlpha',0.5)
creates a
histogram plot with semitransparent bar edges.
EdgeColor
— Histogram edge color
[0 0 0]
or black (default)  '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 threeelement 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 from0
toF
. 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"
Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB^{®} uses in many types of plots.
RGB Triplet Hexadecimal Color Code Appearance [0 0.4470 0.7410]
"#0072BD"
[0.8500 0.3250 0.0980]
"#D95319"
[0.9290 0.6940 0.1250]
"#EDB120"
[0.4940 0.1840 0.5560]
"#7E2F8E"
[0.4660 0.6740 0.1880]
"#77AC30"
[0.3010 0.7450 0.9330]
"#4DBEEE"
[0.6350 0.0780 0.1840]
"#A2142F"
Example: histogram(X,'EdgeColor','r')
creates a
histogram plot with red bar edges.
FaceAlpha
— Transparency of histogram bars
0.6
(default)  scalar value between 0
and
1
inclusive
Transparency of histogram bars, specified as a scalar value
between 0
and 1
inclusive.
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.
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 threeelement 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 from0
toF
. 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"
Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB uses in many types of plots.
RGB Triplet Hexadecimal Color Code Appearance [0 0.4470 0.7410]
"#0072BD"
[0.8500 0.3250 0.0980]
"#D95319"
[0.9290 0.6940 0.1250]
"#EDB120"
[0.4940 0.1840 0.5560]
"#7E2F8E"
[0.4660 0.6740 0.1880]
"#77AC30"
[0.3010 0.7450 0.9330]
"#4DBEEE"
[0.6350 0.0780 0.1840]
"#A2142F"
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.
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 

"."  Dashdotted 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
Normalization
— Type of normalization
'count'
(default)  'probability'
 'countdensity'
 'pdf'
 'cumcount'
 '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
NaN
,NaT
, or<undefined>
values, or if some of the data lies outside the bin limits.
Value  Bin Values  Notes 

'count' (default) 
$${v}_{i}={c}_{i}$$ 

'countdensity' 
$${v}_{i}=\frac{{c}_{i}}{{w}_{i}}$$ 
Note

'cumcount' 
$${v}_{i}={\displaystyle \sum _{j=1}^{i}{c}_{j}}$$ 

'probability' 
$${v}_{i}=\frac{{c}_{i}}{N}$$ 

'pdf' 
$${v}_{i}=\frac{{c}_{i}}{N\text{\hspace{0.17em}}\text{\hspace{0.17em}}\cdot \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{w}_{i}}$$ 
Note

'cdf' 
$${v}_{i}={\displaystyle \sum _{j=1}^{i}\text{\hspace{0.17em}}\frac{{c}_{j}}{N}}$$ 

Example: histogram(X,'Normalization','pdf')
plots
an estimate of the probability density function for X
.
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.
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.
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.
Output Arguments
h
— Histogram
object
Histogram, returned as an object. For more information, see Histogram Properties.
Properties
Histogram Properties  Histogram appearance and behavior 
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: [10000x1 double] Values: [2 2 1 6 7 17 29 57 86 133 193 271 331 421 540 613 ... ] NumBins: 37 BinEdges: [3.8000 3.6000 3.4000 3.2000 3 2.8000 2.6000 ... ] BinWidth: 0.2000 BinLimits: [3.8000 3.6000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0 0 0] 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: [1000x1 double] Values: [1 3 0 6 14 19 31 54 74 80 92 122 104 115 88 80 38 32 ... ] NumBins: 25 BinEdges: [3.4000 3.1200 2.8400 2.5600 2.2800 2 1.7200 ... ] BinWidth: 0.2800 BinLimits: [3.4000 3.6000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0 0 0] 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: [1000x1 double] Values: [3 1 2 15 17 27 53 79 85 101 127 110 124 95 67 32 27 ... ] NumBins: 23 BinEdges: [3.3000 3.0000 2.7000 2.4000 2.1000 1.8000 ... ] BinWidth: 0.3000 BinLimits: [3.3000 3.6000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0 0 0] 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 = 1x27 categorical
Columns 1 through 9
no no yes yes yes no no no no
Columns 10 through 16
undecided undecided yes no no no yes
Columns 17 through 25
no yes no yes no no no yes yes
Columns 26 through 27
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 ... ] Values: [11 14 2] NumDisplayBins: 3 Categories: {'yes' 'no' 'undecided'} DisplayOrder: 'data' Normalization: 'count' DisplayStyle: 'bar' FaceColor: 'auto' EdgeColor: [0 0 0] 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: [1000x1 double] Values: [0.0030 1.0000e03 0.0020 0.0150 0.0170 0.0270 0.0530 ... ] NumBins: 23 BinEdges: [3.3000 3.0000 2.7000 2.4000 2.1000 1.8000 ... ] BinWidth: 0.3000 BinLimits: [3.3000 3.6000] Normalization: 'probability' FaceColor: 'auto' EdgeColor: [0 0 0] 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
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;
Adjust Histogram Properties
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: [1000x1 double] Values: [3 1 2 15 17 27 53 79 85 101 127 110 124 95 67 32 27 ... ] NumBins: 23 BinEdges: [3.3000 3.0000 2.7000 2.4000 2.1000 1.8000 ... ] 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
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
$$f(x,\mu ,\sigma )=\frac{1}{\sigma \sqrt{2\pi}}\text{}\text{exp}[\frac{(x\mu {)}^{2}}{2{\sigma}^{2}}].$$
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((ymu).^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: [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] 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
andfewerbins
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 OutofMemory 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
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