Boxplots

The five-number summary is an abbreviated way to describe a sample. The five number summary is a list of the following numbers:

1. Minimum
2. First (Lower) Quartile,
3. Median,
4. Third (Upper) Quartile,
5. Maximum

The five number summary leads to a graphical representation of a distribution called the boxplot. Boxplots are ideal for comparing two nearly-continuous variables. To draw a boxplot (see the example in the figure below), follow these simple steps:

1. The ends of the box (hinges) are at the quartiles, so that the length of the box is the .
2. The median is marked by a line within the box.
3. The two vertical lines (called whiskers) outside the box extend to the smallest and largest observations within of the quartiles.
4. Observations that fall outside of are called extreme outliers and are marked, for example, with an open circle. Observations between and are called mild outliers and are distinguished by a different mark, e.g., a closed circle.

EXAMPLE: To illustrate boxplots, the figure below puts boxplots side by side of the same four data sets that had histograms in the figure in Week 1.