# Cumulative Frequency Graph

A cumulative frequency graph or ogive of a quantitative variable is a curve graphically showing the cumulative frequency distribution.

#### Example

In the data set faithful, a point in the cumulative frequency graph of the eruptions variable shows the total number of eruptions whose durations are less than or equal to a given level.

#### Problem

Find the cumulative frequency graph of the eruption durations in faithful.

#### Solution

We first find the frequency distribution of the eruption durations as follows. Check the previous tutorial on Frequency Distribution for details.

> duration = faithful\$eruptions
> breaks = seq(1.5, 5.5, by=0.5)
> duration.cut = cut(duration, breaks, right=FALSE)
> duration.freq = table(duration.cut)

We then compute its cumulative frequency with cumsum, add a starting zero element, and plot the graph.

> cumfreq0 = c(0, cumsum(duration.freq))
> plot(breaks, cumfreq0,            # plot the data
+   main="Old Faithful Eruptions",  # main title
+   xlab="Duration minutes",        # xaxis label
+   ylab="Cumulative eruptions")   # yaxis label
> lines(breaks, cumfreq0)           # join the points