MATLAB histogram

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)
fig2plotly()

  h = 
  Histogram with properties:

             Data: [10000x1 double]
           Values: [1x37 double]
          NumBins: 37
         BinEdges: [1x38 double]
         BinWidth: 0.2000
        BinLimits: [-3.8000 3.6000]
    Normalization: 'count'
        FaceColor: 'auto'
        EdgeColor: [0 0 0]

  Show all properties


fig2plotly()

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
fig2plotly()

  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)
fig2plotly()

  h = 
  Histogram with properties:

             Data: [1000x1 double]
           Values: [1x25 double]
          NumBins: 25
         BinEdges: [1x26 double]
         BinWidth: 0.2800
        BinLimits: [-3.4000 3.6000]
    Normalization: 'count'
        FaceColor: 'auto'
        EdgeColor: [0 0 0]

  Show all properties


fig2plotly()

Find the bin counts.

  counts = h.Values
fig2plotly()

  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


fig2plotly()

Change Number of Histogram Bins

Generate 1,000 random numbers and create a histogram.

  X = randn(1000,1);
h = histogram(X)
fig2plotly()

  h = 
  Histogram with properties:

             Data: [1000x1 double]
           Values: [1x23 double]
          NumBins: 23
         BinEdges: [1x24 double]
         BinWidth: 0.3000
        BinLimits: [-3.3000 3.6000]
    Normalization: 'count'
        FaceColor: 'auto'
        EdgeColor: [0 0 0]

  Show all properties


fig2plotly()

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

  Nbins = morebins(h);
Nbins = morebins(h)
fig2plotly()

  Nbins = 29

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

  h.NumBins = 31;
fig2plotly()

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);
fig2plotly()

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';
fig2plotly()

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)
fig2plotly()

  h = 
  Histogram with properties:

              Data: [1x27 categorical]
            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


fig2plotly()

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')
fig2plotly()

  h = 
  Histogram with properties:

             Data: [1000x1 double]
           Values: [1x23 double]
          NumBins: 23
         BinEdges: [1x24 double]
         BinWidth: 0.3000
        BinLimits: [-3.3000 3.6000]
    Normalization: 'probability'
        FaceColor: 'auto'
        EdgeColor: [0 0 0]

  Show all properties


fig2plotly()

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)
fig2plotly()

  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);
fig2plotly()

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;
fig2plotly()

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)
fig2plotly()

  h = 
  Histogram with properties:

             Data: [1000x1 double]
           Values: [1x23 double]
          NumBins: 23
         BinEdges: [1x24 double]
         BinWidth: 0.3000
        BinLimits: [-3.3000 3.6000]
    Normalization: 'count'
        FaceColor: 'auto'
        EdgeColor: [0 0 0]

  Show all properties


fig2plotly()

Specify exactly how many bins to use.

  h.NumBins = 15;
fig2plotly()

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];
fig2plotly()

Change the color of the histogram bars.

  h.FaceColor = [0 0.5 0.5];
h.EdgeColor = 'r';
fig2plotly()

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')
fig2plotly()

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 σ2 is

  None

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)
fig2plotly()

Saving and Loading Histogram Objects

Use the savefig function to save a histogram figure.

  histogram(randn(10));
savefig('histogram.fig');
close gcf
fig2plotly()

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

  h = openfig('histogram.fig');
fig2plotly()

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')
fig2plotly()

  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


fig2plotly()

MATLAB - histogram

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

Plot Multiple Histograms

Adjust Histogram Properties

Determine Underlying Probability Distribution

Saving and Loading Histogram Objects

MATLAB - `histogram`