# Cumulative Frequency Distribution

The cumulative frequency distribution of a quantitative variable is a summary of data frequency below a given level.

#### Example

In the data set faithful, the cumulative frequency distribution of the eruptions variable shows the total number of eruptions whose durations are less than or equal to a set of chosen levels.

#### Problem

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

#### Solution

We first find the frequency distribution of the eruption durations as follows. Further details can be found in the Frequency Distribution tutorial.

> 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 apply the cumsum function to compute the cumulative frequency distribution.

> duration.cumfreq = cumsum(duration.freq)

The cumulative distribution of the eruption duration is:

> duration.cumfreq
[1.5,2) [2,2.5) [2.5,3) [3,3.5) [3.5,4) [4,4.5) [4.5,5)
51      92      97     104     134     207     268
[5,5.5)
272

#### Enhanced Solution

We apply the cbind function to print the result in column format.

> cbind(duration.cumfreq)
duration.cumfreq
[1.5,2)               51
[2,2.5)               92
[2.5,3)               97
[3,3.5)              104
[3.5,4)              134
[4,4.5)              207
[4.5,5)              268
[5,5.5)              272

#### Exercise

Find the cumulative frequency distribution of the eruption waiting periods in faithful.