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Part II: Number-Crunching Basics
The median, part of the five-number summary, is shown by the line that cuts
through the box in the boxplot. This makes it very easy to identify. The mean,
however, is not part of the boxplot and can’t be determined accurately by
just looking at the boxplot.
You don’t see the mean on a boxplot because boxplots are based completely
on percentiles. If data are skewed, the median is the most appropriate mea-
sure of center. Of course you can calculate the mean separately and add it to
your results; it’s never a bad idea to show both.
Investigating Old Faithful’s boxplot
The relevant descriptive statistics for the Old Faithful geyser data are found
in Figure 7-10.
Figure 7-10: Picking out the center using the median
Descriptive Statistics: Time between Eruptions
Descriptive
statistics for Total
Q1
Mean
Q3
IQR
Old Faithful Variable Count 71.009 StDev Minimum 60.000 Median 81.000 Maximum 21.000
Time between
222
75.000
95.000
12.799
42.000
data.
You can predict from the data set that the shape will be skewed left a bit because
the mean is lower than the median by about 4 minutes. The IQR is Q – Q =
3 1
81 – 60 = 21 minutes, which shows the amount of overall variability in the time
between eruptions; 50% of the eruptions are within 21 minutes of each other.
A vertical boxplot for length of time between eruptions of the Old Faithful
geyser is shown in Figure 7-11. You confirm that the data are skewed left
because the lower part of the box (where the small values are) is longer than
the upper part of the box.
You see the values of the boxplot in Figure 7-11 that mark the five-number
summary and the information shown in Figure 7-10, including the IQR of 21
minutes to measure variability. The center as marked by the median is 75
minutes; this is a better measure of center than the mean (71 minutes), which
is driven down a bit by the left skewed values (the few that are shorter times
than the rest of the data).
Looking at the boxplot (Figure 7-11), you see there are no outliers denoted by
stars. However, note that the boxplot doesn’t pick up on the bimodal shape
of the data that you see in Figure 7-5. You need a good histogram for that.

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