Area of a histogram plot

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Value Summary

OptionalNon-negative real number

Graphics Primitives

ObjectsArea Default Values


Area determines whether bars of a histogram plot are scaled with respect to their heights or with respect to their areas, and by how much.

By default, the bars of a histogram plot use a height that is equal to the absolute number of data points in he corresponding cell. Using Area, the user can change this behavior to make the areas of the bars proportional to this number.


Example 1

For any distribution with a continuous quantile, we can define, using stats::equiprobableCells, a list of n cells where each cell is “hit” with the same probability, . By the law of large numbers, we expect the number of elements in each cell to be approximating for large values of N, the number of samples:

X := stats::normalRandom(10, 1):
cells := stats::equiprobableCells(40,
            stats::normalQuantile(10, 1)):
N := 1000:
data := [X() $ i = 1..N]:
plot(plot::Histogram2d(data, Cells = cells))

N := 10000:
data := [X() $ i = 1..N]:
plot(plot::Histogram2d(data, Cells = cells))

On the other hand, if we want to display a histogram as an approximation to the probability distribution, we want not the height, but rather the area of the rectangles to correspond to our measurements. Moreover, the sum of all areas should be 1, so we set Area to this value:

plot(plot::Histogram2d(data, Cells = cells, Area = 1))

plot(plot::Histogram2d(data, Cells = cells, Area = 1),
     plot::Function2d(stats::normalPDF(10,1)(x), x = 7..13,
                      Color = RGB::Black, LineWidth = 0.5))

See Also

MuPAD Functions