# Relative Frequency Distribution of Quantitative Data

The relative frequency distribution of a data variable is a summary of the frequency proportion in a collection of non-overlapping categories.

The relationship of frequency and relative frequency is:

#### Example

In the data set faithful, the relative frequency distribution of the eruptions variable shows the frequency proportion of the eruptions according to a duration classification.

#### Problem

Find the relative 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)

Then we find the sample size of faithful with the nrow function, and divide the frequency distribution with it. As a result, the relative frequency distribution is:

> duration.relfreq = duration.freq / nrow(faithful)

The frequency distribution of the eruption variable is:

> duration.relfreq
duration.cut
[1.5,2)  [2,2.5)  [2.5,3)  [3,3.5)  [3.5,4)  [4,4.5)
0.187500 0.150735 0.018382 0.025735 0.110294 0.268382
[4.5,5)  [5,5.5)
0.224265 0.014706

#### Enhanced Solution

We can print with fewer digits and make it more readable by setting the digits option.

> old = options(digits=1)
> duration.relfreq
duration.cut
[1.5,2) [2,2.5) [2.5,3) [3,3.5) [3.5,4) [4,4.5) [4.5,5)
0.19    0.15    0.02    0.03    0.11    0.27    0.22
[5,5.5)
0.01
> options(old)    # restore the old option

We then apply the cbind function to print both the frequency distribution and relative frequency distribution in parallel columns.

> old = options(digits=1)
> cbind(duration.freq, duration.relfreq)
duration.freq duration.relfreq
[1.5,2)            51             0.19
[2,2.5)            41             0.15
[2.5,3)             5             0.02
[3,3.5)             7             0.03
[3.5,4)            30             0.11
[4,4.5)            73             0.27
[4.5,5)            61             0.22
[5,5.5)             4             0.01
> options(old)    # restore the old option

#### Exercise

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