This distribution is skewed left because the tail is to the left. If the tail were to the right, the graph would
be described at skewed right .
There are four types of graph we want to look at in order to help us understand the shape of a
distribution: dotplot, stemplot, histogram, and boxplot. We use the following 31 scores from a 50-point
quiz given to a community college statistics class to illustrate the first three plots (we will look at a
boxplot in a few pages):
Dotplot
A dotplot is a very simple type of graph that involves plotting the data values, with dots, above the
corresponding values on a number line. A dotplot of the scores on the statistics quiz, drawn by a statistics
computer package, looks like this:
[Calculator note: Most calculators do not have a built-in function for drawing dotplots. There are
work-arounds that will allow you to draw a dotplot on a calculator, but they involve more effort than they
are worth.]
Stemplot (Stem and Leaf Plot)
A stemplot is a bit more complicated than a dotplot. Each data value has a stem and a leaf . There are no
mathematical rules for what constitutes the stem and what constitutes the leaf . Rather, the nature of the
data will suggest reasonable choices for the stem and leaves. With the given score data, we might choose
the first digit to be the stem and the second digit to be the leaf . So, the number 42 in a stem and leaf plot
would show up as 4|2. All the leaves for a common stem are often on the same line. Often, these are listed
in increasing order, so the line with stem 4 could be written as: 4 | 0112236. The complete stemplot of the
quiz data looks like this: