Like histograms, dotplots are used to understand the pattern underlying a data set. Are most of the values large? Are most small? Unlike a histogram, the dotplot also shows you information about individual data values. So while a histogram can’t be used to answer the question “how many data values were 10?”, a dotplot can!
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So, let’s use an example to see how to make a nice dotplot. Note that many technology tools like Minitab can be used to create dotplots, but you may find in your typical statistics course you are making them by hand. Further, making a plot by hand is always a great way to get better at reading them.
Sketching a dotplot
The following data set shows the fuel economy (in miles per gallon) for a sample of 2015 model year vehicles.
| Vehicle | Fuel Economy | Vehicle | Fuel Economy | Vehicle | Fuel Economy | Vehicle | Fuel Economy |
|---|---|---|---|---|---|---|---|
| Aston Martin V8 Vantage S | 16 | Hyundai Elantra | 32 | Kia Forte | 31 | Honda Accord | 31 |
| BMW 528i | 27 | Chevrolet Cruze | 30 | Buick Regal | 24 | Mazda 6 | 32 |
| Subaru Legacy | 30 | Toyota Corolla | 31 | Lincoln MKZ Hybrid | 40 | Dodge Challenger | 23 |
| Dodge Dart | 31 | Lexus GS 450h | 31 | Subaru Impreza | 31 | Volvo V60 FWD | 29 |
Now this data set definitely includes a wide variety of cars (although it is a bit of a small sample). It will be interesting to see the plot!
Step 1: Choose a scale and set it up.
We are going to make a horizontal scale and it needs to cover all values. For this data set, the smallest value is 16 and the largest is 40.
You will notice that I chose to count by 2 instead of 1. This isn’t required but just makes the plot a little more compact. You can count by 1, 5, or even 10 if you like!
Step 2: Plot the dots.
Alright, this step sounds goofy but there is really no other way to say it. For this step, you will start filling in the dots using your scale. Remember: Each value gets a dot and dots are “stacked”. To see this, let’s start by plotting only the first row of data.
| Vehicle | Fuel Economy | Vehicle | Fuel Economy | Vehicle | Fuel Economy | Vehicle | Fuel Economy |
|---|---|---|---|---|---|---|---|
| Aston Martin V8 Vantage S | 16 | Hyundai Elantra | 32 | Kia Forte | 31 | Honda Accord | 31 |
You can see that each value is represented by a dot on the plot and that, since there were two cars that get 31 mpg, we put two dots on top of each other. Now we can continue the process with the rest of the data. Remember that while you can’t be perfect doing this by hand, that you should try and make sure that the dots mostly line up. You don’t want any big spaces between dots to make one value look more common than another.
Here is the data set along with the finished dotplot. You can see again, each value got a dot. Notice that we added a title and a label to our main scale. This step is important so someone else looking at the plot can know what kind of data they are looking at.
| Vehicle | Fuel Economy | Vehicle | Fuel Economy | Vehicle | Fuel Economy | Vehicle | Fuel Economy |
|---|---|---|---|---|---|---|---|
| Aston Martin V8 Vantage S | 16 | Hyundai Elantra | 32 | Kia Forte | 31 | Honda Accord | 31 |
| BMW 528i | 27 | Chevrolet Cruze | 30 | Buick Regal | 24 | Mazda 6 | 32 |
| Subaru Legacy | 30 | Toyota Corolla | 31 | Lincoln MKZ Hybrid | 40 | Dodge Challenger | 23 |
| Dodge Dart | 31 | Lexus GS 450h | 31 | Subaru Impreza | 31 | Volvo V60 FWD | 29 |
That really is it! The dotplot is a great plot to use for representing data precisely because it is so simple to make and read. Remember that in statistics, our goal is often to communicate information to others. The more simply we can do this, the better.
For some examples of the types of questions you might run across when it comes to dotplots and what information you can gather from them, check out “How to read a dotplot” next.