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Scilab Help >> Statistics > Descriptive Statistics > histc


computes an histogram


[cf, ind] = histc(n, data [,normalization])
[cf, ind] = histc(x, data [,normalization])



positive integer (number of classes)


increasing vector defining the classes (x may have at least 2 components)


vector (data to be analysed)


vector representing the number of values of data falling in the classes defined by n or x


vector or matrix of same size as data, representing the respective belonging of each element of data data to the classes defined by n or x


scalar boolean. normalization=%t (default): cf represents the number of points in each class, relatively to the total number of points, normalization=%f: cf represents the total number of points in each class


This function computes a histogram of the data vector using the classes x. When the number n of classes is provided instead of x, the classes are chosen equally spaced and x(1) = min(data) < x(2) = x(1) + dx < ... < x(n+1) = max(data) with dx = (x(n+1)-x(1))/n.

The classes are defined by C1 = [x(1), x(2)] and Ci = ( x(i), x(i+1)] for i >= 2. Noting Nmax the total number of data (Nmax = length(data)) and Ni the number of data components falling in Ci, the value of the histogram for x in Ci is equal to Ni/(Nmax (x(i+1)-x(i))) when "normalized" is selected and else, simply equal to Ni. When normalization occurs the histogram verifies:

when x(1)<=min(data) and max(data) <= x(n+1)


  • Example #1: variations around a histogram of a gaussian random sample
    // The gaussian random sample
    d = rand(1, 10000, 'normal');
    [cf, ind] = histc(20, d, normalization=%f)
    // We use histplot to show a graphic representation
    clf(); histplot(20, d, normalization=%f);
    [cf, ind] = histc(20, d)
    clf(); histplot(20, d);
  • Example #2: histogram of a binomial (B(6,0.5)) random sample
    d = grand(1000,1,"bin", 6, 0.5);
    c = linspace(-0.5,6.5,8);
    [cf, ind] = histc(c, d)
    histplot(c, d, style=2);
    xtitle(_("Normalized histogram"))
    [cf, ind] = histc(c, d, normalization=%f)
    histplot(c, d, normalization=%f, style=5);
    xtitle(_("Non normalized histogram"))
  • Example #3: histogram of an exponential random sample
    lambda = 2;
    X = grand(100000,1,"exp", 1/lambda);
    Xmax = max(X);
    [cf, ind] = histc(40, X)
    histplot(40, X, style=2);
    x = linspace(0, max(Xmax), 100)';
    plot2d(x, lambda*exp(-lambda*x), strf="000", style=5)
    legend([_("exponential random sample histogram") _("exact density curve")]);
  • Example #4: the frequency polygon chart and the histogram of a gaussian random sample
    n = 10;
    data = rand(1, 1000, "normal");
    [cf, ind] = histc(n, data)
    clf(); histplot(n, data, style=12, polygon=%t);
    legend([_("normalized histogram") _("frequency polygon chart")]);

See also

  • histplot — plot a histogram
  • hist3d — 3D representation of a histogram
  • plot2d — 2D plot
  • dsearch — distribute, locate and count elements of a matrix or hypermatrix in given categories


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