2.10: Graphing Quantitative Data- Means Plot

New type of graph alert! Means plots are not like the other types of graphs that we've been learning. Because means are quantitative, a means plot is a type of graph showing quantitative data. This could be confusing, though, because the groups are qualitative variables.

Exercise \(\PageIndex{1}\)

If a means plot shows the means of different groups in a graph, how are they different from the other graphs that we've learned about?

Answer

Your answer should mention that most of the graphs that we've been learning are frequency graphs, meaning that they show the frequency of each score. However, a means plot only shows the means of different groups.

Figure \(\PageIndex{1}\) shows a means plot of GPA for Duke University students by their major. Notice that this is not showing the frequency of academic majors, nor is it showig the frequency of individual GPAs. Instead, it is showing the mean GPA for the three categories of academic majors.

Figure \(\PageIndex{1}\): Means Plot of Average GPA by Academic Majors. (Copyright CC-SA, chart by Dr. MO via data provided by OpenIntro.org )

Like with a frequency bar chart for qualitative variables, the x-axis show the qualitative variable's categories. In Figure \(\PageIndex{1}\), that is academic major. While these are in alphabetical order (A for Arts, N for Natural, S for Social), they could be ordered in any way that you'd like since the categories are qualitative variables and don't have a natural order. Different from a frequency bar chart, the y-axis of a means plot shows the average of the quantitative variable. For Figure \(\PageIndex{1}\), that is the mean GPA for each category of academic major.

Sometimes you'll see the means plotted like a line graph, as shown in Figure \(\PageIndex{2}\). This is the exact same data as in Figure \(\PageIndex{1}\), just displayed as dots that are connected by a line.

Figure \(\PageIndex{2}\): Means Plot of Average GPA by Academic Majors. (Copyright CC-SA, chart by Dr. MO via data provided by OpenIntro.org )

Even though Figure \(\PageIndex{2}\) looks like a line graph or frequency polygon, it does not make sense to try to describe the shape of the distribution (kurtosis) or skew since this isn't a distribution of all of the data. However, we can still interpret what the graph is telling us. Both Figure \(\PageIndex{1}\) and Figure \(\PageIndex{2}\) show that the average GPA is pretty similar between the types of majors, but that the average GPA of Natural Science majors might be a little higher.

Means Plot Interpretation

Most, but not all, of the questions that we've been answering to help interpret graphs make sense for a means plot since we are only looking at group means, not frequencies or the shape of a distribution.

1. What kind of graph is Figure \(\PageIndex{1}\) or Figure \(\PageIndex{2}\)?
   1. Both of these graphs are means plots, which show the average score on a quantitative variable for qualitative groups.
2. What does the x-axis measure in Figure \(\PageIndex{1}\) or Figure \(\PageIndex{2}\)?
3. 1. The x-axis on means plots show categories of the qualitative variable. In these charts, the qualitative categories are based on academic major.
4. What does the y-axis measure in Figure \(\PageIndex{1}\) or Figure \(\PageIndex{2}\)?
   1. The y-axis is the axis that goes up and down. Unlike most charts discussed in this textbook, the y-axis in means plots is the average score on the quantitative variable. For our data, this is GPA.
5. Is Figure \(\PageIndex{1}\) or or Figure \(\PageIndex{2}\) skewed? If so positively or negatively? If not, is the graph tall/narrow, medium/normal, or wide/flat?
   1. This questions doesn't make sense for means plots since the x-axis categories could be plotted in any order.
6. What do you notice from Figure \(\PageIndex{1}\)? What pops out to you?
   1. I notice that the means look pretty similar based on the scale of the y-axis (from a GPA of 3.00 to 4.00), but that Natural Sciences does look a little higher than the other two groups of majors.
7. What does Figure \(\PageIndex{1}\) or Figure \(\PageIndex{2}\) make you wonder about?
   1. This means plot makes me wonder why Natural Sciences have a little higher GPA. Are the instructors better in those fields? Do the students have more study skills?
8. What is a catchy headline for Figure \(\PageIndex{1}\) or Figure \(\PageIndex{2}\)?
   1. Major isn't Major (because academic major doesn't affect GPA)
9. How could you summarize the info in Figure \(\PageIndex{1}\) or Figure \(\PageIndex{2}\)into one sentence?
   1. GPA is pretty similar between academic majors, although Natural Science majors might have slightly higher average GPAs.
10. Who might want to know the information in Figure \(\PageIndex{1}\) or Figure \(\PageIndex{2}\)?
    1. I imagine that Duke University students would be interested in this information, as well as Duke University administrators. As a professor, Dr. MO would also be interested in this! She might work even harder to help her students to try to have the Social Sciences have the highest average GPA.

Summary

Means plots aren't complex but they feel tricky because they look like bar charts or line graphs, but show very different information (means, instead of frequencies). We won't talk about them for awhile, but keep them in mind when we start comparing multiple means in Unit 3 (More Mean Differences).

Figure \(\PageIndex{1}\): The surprisingly logical minds of babies TED Talk

This TED Talk (Shulz, 2015) shows means plots in actions, and previews how we'll use probability in analyzing our data. It's about babies!

Figure \(\PageIndex{1}\): Laura Shulz's TED Talk about research on how babies think. (CC-BY-NC-ND TED Talks)

We have a few more types of graphs for quantitative variables to learn about. Let's go!

Contributors

• Dr. MO (Taft College)