1.05 Dot plots and stem plots

Dot plots are a graphical way of displaying the frequencies of discrete quantitative or categorical data. In other words, they show how often a particular choice was made or how many times an event occured. They are best used for small to medium size sets of data and are good for visually highlighting how the data is spread and whether there are any outliers that may change our measures of central tendency, particularly the mean and the median.

We start off with a list of all the possible outcomes in our study, and add dots for each data point in the set. For example, if the number of children in peoples' families ranged between 1 and 5, our dot plot might look like the following:

Each of the possible outcomes is written on a number line. The number of dots above each score corresponds to the frequency of each score. For example, in the dot plot above, we can see that 3 families have one child, 8 families have two children and so on.

Examples

Example 1

The goals scored by a football team in their matches are represented in the following dot plot.

Complete the following frequency distribution table.

Goals scored	Frequency
0	⬚
1	⬚
2	⬚
3	⬚
4	⬚
5	⬚

Worked Solution

Create a strategy

The number of dots in each column corresponds to the number of matches in which the particular number of goals labelled at the bottom of the column were scored.

Apply the idea

By checking the number of dots of each column, we can fill in the frequency of each goal scored.

Goals scored	Frequency
0	1
1	9
2	8
3	7
4	9
5	3

Watch question walkthrough

Stem plots (sometimes called stem-and-leaf plots) are a great way to display moderately sized data sets, as they give a good overview of the shape of the data. This means we can identify any symmetry, skew, outliers and/or clustering. Further, since each individual score is recorded in a stem plot, they also make it easy to identify the mode in a data set.

In stem plots, the last digit in a score is split from the other digits in the score. The last digit becomes the "leaf" and the other digits become the "stem."

Notice how the stem is a column and the stem values are written downwards in that column. The leaf values are written across in the rows corresponding to the stem value. The leaf values are written in ascending order from the stem outwards.

The stem is used to group the scores and each leaf indicates the individual scores within each group.

Notice that all the scores are written in ascending order. When creating stem plots it can be easier to first sort all the scores in order from smallest to largest.

Examples