### 7.1.12 Cumulative frequencies: cumulated_frequencies frequences_cumulees

Given a list, the cumulated_frequencies command will plot
the cumulated frequency of the numbers in the list; i.e., the area
under the resulting graph at a value x will be the fraction of
numbers less than x. For example, if you enter

cumulated_frequencies([1,2,1,1,2,1,2,4,3,3])

then you will get

The cumulated_frequencies command can also take a matrix
with two columns as an argument. In this case, the first column will
represent values while the second column will represent the number of
times the values occur. For example, the above graph can be drawn
with the command

cumulated_frequencies([[1,4],[2,3], [3,2], [4,1]])

If the first column of the input matrix contains intervals
a..b instead of numbers, then the second column values will
be normalized to add up to one, and will represent the frequencies of
the intervals. If the matrix has the form

[[a_{0}..a_{1},f_{1}],...,[a_{n−1}..a_{n},f_{n}]] |

then the plot will consist of the polygonal path starting at (a_{0},0)
and moving to (a_{1},f_{1}) to (a_{2},f_{1}+f_{2}) and so on until
(a_{n},f_{1}+⋯ + f_{n}). For example, both

cumulated_frequencies([[1..2,30],[2..4,40],[4..5,30]])

and

cumulated_frequencies([[1..2,03],[2..4,0.4],[4..5,0.3]])

will give you

If the matrix given to cumulated_frequencies has more than
two columns, then each additional column will represent a different
distribution of the numbers in the first column, and each distribution
will be graphed. For example, if you enter

cumulated_frequencies([[1,4,1],[2,3,4], [3,2,1], [4,1,2]])

then both the distributions given by
[[1,4],[2,3], [3,2], [4,1]]
and
[[1,1],[2,4], [3,1], [4,2]]
will be drawn on the same axes; the result will be