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A boxplot is a graphical summary based on the median, quartiles, and extreme values. To display the downtime data given in Example 1.1 using a boxplot, write

boxplot(downtime)

which gives Fig. 3.1. Often called the Box and Whiskers Plot, the box represents the interquartile range that contains 50% of cases. The whiskers are the lines that extend from the box to the highest and lowest values. The line across the box indicates the median.

Figure 3.1 A Simple Boxplot

To improve the look of the graph, we could label the axes as follows:

boxplot(downtime, xlab = "Downtime", ylab = "Minutes")

which gives Fig. 3.2.

Figure 3.2 A Boxplot with Axis Labels

Multiple boxplots can be displayed on the same axis, by adding extra arguments to the boxplot function. For example,

boxplot(results$arch1, results$arch2, xlab = "Architecture Semesters 1 and 2")

or simply

boxplot(arch1, arch2, xlab = "Architecture Semesters 1 and 2")

gives Fig. 3.3.

Figure 3.3 Multiple Boxplots

Figure 3.3 allows us to compare the performance of the students in Architecture in the two semesters. It shows, for example, that the marks are lower in Architecture in Semester 2 and the range of marks is narrower than those obtained in Architecture in Semester 1.

Notice also in Fig. 3.3 that there are points outside the whiskers of the boxplot in Architecture in Semester 2. These points represent cases over 1.5 box lengths from the upper or lower end of the box and are called outliers. They are considered atypical of the data in general, being either extremely low or extremely high compared to the rest of the data.

Looking at Exercise 1.1 with the uncorrected data, Fig. 3.4 is obtained using

boxplot(marks˜gendermarks)

Figure 3.4 A Gender Comparison

Notice the outlier in Fig. 3.4 in the male boxplot, a value that appears large compared to the rest of the data. You will recall that a check on the examination results indicated that this value should have been 46, not 86, and we corrected it using

marks[34] <- 46

Repeating the analysis, after making this correction

boxplot(marks˜gendermarks)

gives Fig. 3.5.

Figure 3.5 A Gender Comparison (corrected)

You will now observe from Fig. 3.5 that there are no outliers in the male or female data. In this way, a boxplot may be used as a data validation tool. Of course, it is possible that the mark of 86 may in fact be valid, and that a male student did indeed obtain a mark that was much higher than his classmates. A boxplot highlights this and alerts us to the possibility of an error.

To compare the performance of females and males in Architecture in Semester 1, write

gender <- factor(gender, levels = c("f", "m"), labels = c("Female", "Male"))

which changes the labels from “f ” and “m” to “Female” and “Male,” respectively. Then

boxplot(arch1∼gender, ylab = "Marks (%)", main = "Architecture Semester 1", font.main = 1)

outputs Fig. 3.6.

Figure 3.6 A Gender Comparison

Notice the effect of using main = "Architecture Semester 1" that puts the title on the diagram. Also, the use of font.main = 1 ensures that the main title is in plain font.

We can display plots as a matrix using the par function: par(mfrow = c(2,2)) causes the outputs to be displayed in a array.

par(mfrow = c(2,2)) boxplot(arch1∼gender, main = "Architecture Semester 1", font.main = 1) boxplot(arch2∼gender, main = "Architecture Semester 2", font.main = 1) boxplot(prog1∼gender, main = "Programming Semester 1", font.main = 1) boxplot(prog2∼gender, main = "Programming Semester 2", font.main = 1)

produces Fig. 3.7.

Figure 3.7 A Lattice of Boxplots

We see from Fig. 3.7 that female students seem to do less well than their male counterparts in Programming in Semester 1, where the median mark of the females is considerably lower than that of the males: it is lower even than the first quartile of the male marks. In the other subjects, there do not appear to be any substantial differences.

To undo a matrix‐type output, write

par(mfrow = c(1,1))

which restores the graphics output to the full screen.