Scatterplot

1. Scatterplots

Scatterplots are ways that you can show more than one quantitative attribute at a time for a particular data set. In the past, you’ve been using something like dot plots, where you have a particular quantitative attribute about a data set. In addition, you've been making dot plots where you stack up dots at a particular value, and you look at it that way.

However, scatterplots allow you not only to see how those values compare along with one attribute but also along with a different attribute.

EXAMPLE

You might put the two variables cigarette consumption and cancer death in a scatterplot. Perhaps certain states or countries have low cigarette consumption and maybe, correspondingly, low cancer deaths. Each dot would correspond to one single state or one single country.

EXAMPLE

If you were going with a sports team, maybe you'd want to know if spending a lot of money on your team payroll causes them to win more. Each dot, in that case, would correspond to a single team.

IN CONTEXT

This was the 1992 payrolls for the National Football League for their quarterback, who's usually their most expensive player, and for the entire team. The values are in thousands of dollars.

Team	QB Salary	Total Payroll		Team	QB Salary	Total Payroll
49ers	900	17,256		Falcons	2,250	25,642
Bears	3,000	23,074		Giants	1,600	23,258
Bengals	1,050	20,666		Jets	800	19,063
Bills	650	24,249		Lions	1,525	24,644
Broncos	500	21,992		Oilers	1,700	21,399
Browns	967	19,413		Packers	1,500	23,245
Buccaneers	675	19,545		Patriots	2,250	23,294
Cardinals	1,450	20,397		Raiders	1,300	20,390
Chargers	1,200	18,698		Rams	1,500	24,378
Chiefs	1,100	25,859		Redskins	1,450	20,780
Colts	2,000	22,022		Saints	1,200	23,695
Cowboys	1,750	28,349		Seahawks	1,250	25,348
Dolphins	1,400	23,728		Steelers	3,500	30,131
Eagles	425	19,325		Vikings	1,250	23,246

Next, let's put this on a scatterplot. The value that should go on the x-axis, or the horizontal axis, should be the one that you think helps to explain the other variable. It is most likely the quarterback salary that helps to contribute to a high or low team salary.

Start with the first team, the 49ers. Find that $900,000 for the quarterback and $17.2 million for the team payroll and put a dot there. That's one of the many dots that we're going to end up with.



The next team, the Bears, had a quarterback salary of $3 million and a total payroll of about $23 million. As you continue with the rest of the teams, you’re going to end up with one dot for each team. The final version looks like this:



It seems that as the quarterback salary increases, as it moves to the right, the total payroll tends to increase as well.

hint

You can also see this using technology. If you want to use Excel, all you have to do is enter the data, select the area that you want, and pick the correct graph of scatterplot.

You may need to add labels to the axes and sometimes there's a bit of extraneous stuff that you can get rid of. Overall, though, you can see that same set of data.

term to know

Scatterplot

A graphical display that allows us to see the relationship between two quantitative variables.

2. Multiple Data Sets

A great thing about scatterplots is that you can easily show multiple data sets onto one plot. The way this is done is by using different symbols to represent the different data sets.

EXAMPLE

Recall the in-context scenario from the previous section that compared quarterback salary to total team payroll. Suppose that you wanted to add an additional categorical variable. You want to know if the payrolls are different depending on conferences. There are two conferences in the National Football League, the NFC and the AFC.

What you can do is use the same data, split the data between the two conferences, and use different symbols for AFC (a gray circle) or NFC (a blue square).

You'll notice that it is the same scatterplot as before, however, the data points are separated by the two conferences and this is visible with the two different symbols.

term to know

Multiple Data Sets

Plotting more than one data set on a scatterplot requires that we use different colors or symbols for the different data sets so we can see the relationships separately.