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Scatterplot
Common Core: 8.SP.1

Scatterplot

Author: Sophia Tutorial
Description:

Determine data points using a scatterplot.

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Tutorial
what's covered
This tutorial will discuss the topic of scatterplots. Our discussion breaks down as follows:

  1. Scatterplots
  2. Multiple Data Sets


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.

Scatter Plot for Countries: Cigarette Consumption vs. Cancer Deaths

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.

Scatter Plot for Sports Team: Payroll vs. Wins

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.

Plotting the salary of the quarterback and the total team salary for the 49ers.

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:

Plotting the salary of the quarterback and total team salary for all teams.

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).

Plotting the salary of the quarterback and total team salary for AFC teams vs. NFC teams.
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.

summary
Scatterplots are ways that you can show more than one quantitative attribute at a time for a particular data set. It is a way to show the relationship between two quantitative variables, which are paired data sets. These are two attributes for the same individuals in the data set. One variable, typically the one that we think might cause the other to happen, is assigned to the x-axis. The other is assigned to the y-axis. It's also possible to put in multiple data sets, just using different symbols or different colors, to denote the different sets.

Good luck!

Source: Adapted from Sophia tutorial by Jonathan Osters.

Terms 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.

Scatterplot

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