Classes of histogram plots

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Value Summary

MandatoryList of arithmetical expressions

Graphics Primitives

ObjectsCells Default Values


Cells determines the number and position of the classes used in a histogram.

Cells accepts either a single positive integer (or, equivalently, a list of one positive integer) or a list of cells given as ranges or lists of two elements.

A single integer n in the specification Cells = n or Cells = [n] is interpreted as “subdivide the range of data into n cells of equal size.”

The number n can be animated. In this case, n may be a symbolic expression of the animation parameter.

The cells may be specified directly as in Cells = [[a1, b1], [a2, b2], …] or Cells = [a_1..b_1, a_2..b_2, Symbol::dots].


The i-th cell is the semi-open interval , i.e., a datum x is tallied into the i-th cell if ai < xbi is satisfied.

The cell boundaries must satisfy a1 < b1a2 < b2a3 < …. In most applications, b1 = a2, b2 = a3 etc. is appropriate.

If giving cells directly, the leftmost border may be - infinity and the rightmost border may be infinity. These rectangles will then be adjusted according to the average widths of the other rectangles for display purposes.

With the attribute CellsClosed = Left, the cells [a_1..b_1, a_2..b_2, Symbol::dots] are interpreted as the semi-open intervals .


Example 1

We create a sample of 1000 data points and plot a histogram of them:

X := stats::fRandom(100, 10):
data := [X() $ i = 1..1000]:

The shape of the distribution becomes much better visible when we increase the number of cells:

plot(plot::Histogram2d(data, Cells = 40))

plot(plot::Histogram2d(data, Cells = [40], Area = 1),
     plot::Function2d(stats::fPDF(100,10)(x), x = 0 .. 5,
                      Color = RGB::Black))

With cells of different widths, setting Area to a positive value is highly recommended, to still have the histogram follow the probability distribution:

cells :=  stats::equiprobableCells(50,
                  stats::fQuantile(100, 10))
plot(plot::Histogram2d(data, Cells = cells)):

plot(plot::Histogram2d(data, Cells = cells, Area = 1),
     plot::Function2d(stats::fPDF(100, 10)(x), x = 0 .. 5,
                      Color = RGB::Black))

See Also

MuPAD Functions