Using the Right Kind of Graph to Show Your Data

From a young age, students are asked to show the data they have collected in various forms of charts, tables, graphs, and plots. With so many different ways to show your data, how do you know which one will be most representative and accurate of what you've found? Never fear, the data displayer is here!

There are three main ways we can show our data:

1. Using pictures of real objects - picture graphs and concrete graphs;

2. Using symbols - pictographs, tally charts and frequency tables;

3. Using abstract representations - bar graphs, stem-and-leaf plots, line graphs, scatter plots, circle graphs, box plots.

Since there are a lot more different ways to represent data abstractly, I will focus on these.

Bar Graphs

A bar graph is a chart that uses the length or height of bars to represent quantities, often the number of occurrences of particular responses. Bar graphs are used to display discrete data, meaning the data can only take certain values that can be counted. The number of possible values is also limited. A Maths Dictionary for Kids further expands on this definition.

Chela5808. (2009, January 1). Bargraph [Online Image]. Retrieved from http://wikieducator.org/File:Bargraph.jpg.

However, there are variations of bar graphs that do record continuous data; specifically, data that can be refined to be more specific. The Minitab Blog provides a good definition and some examples of both continuous and discrete data.

A histogram and stem-and-leaf plots are both examples of variations of bar graphs that represent continuous data. The categories along the horizontal axis are always continuous number intervals, and therefore the bars in this graph are touching to show this continuity. Stem-and-leaf plots are most appropriate when numerical data are best organized by place value. They show the number of occurrences of data in each interval as well as an individual piece of data. Examples of both are shown.

Statistics Canada. (2013, July 23). Example of a histogram [Online Image]. Retrieved from http://bit.ly/2zR5Nl2

Yale University. (2008, June). Example of a stem-and-leaf plot [Online Image].
Retrieved from http://bit.ly/2mE78H0

Line Graphs

Line graphs, also known as broken-line graphs, are used to show trends in data but connecting plotted points that are not in a straight line. The points are plotted to show how one variable is related to the other (Small, pp. 601). One of our variables is always continuous, typically time.

Markes, A. (2017, November 18). Example of a line graph [Graph].

Scatter Plots
Scatter plots are similar to line graphs in that they use the horizontal and vertical axes to plot points (Illinois Education). What's special about this type of graph is its purpose to show how much one variable is affected by the other. The closer the data points are plotted to make a straight line, the stronger the relationship between the two variables. Therefore, you would use this type of graph when you want to see a pattern, trend or relationship between the two variables.

Markes, A. (2017, November 18). Example of a scatter plot [Graph].

Circle Graphs

A circle graph is a circle that is divided into sections or categories. The main function of a circle graph is two-fold: (1) show the relationships among parts of a whole and (2) show the relationships between each part to the whole (Small, pp. 603). This graph is most often used when it is important to see how a total amount is distributed.

Statistics Canada. (2013, July 23). "Example of a circle graph" [Online Image].
Retrieved from http://bit.ly/2iufSeh

For any graph you create, make sure you include a meaningful title and label all axes and legends clearly so as to guide the reader in interpreting it accurately.

I don't trust people with graph paper; they're always plotting something.