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4 Tutorials that teach Scatterplot
Common Core: 8.SP.1

# Scatterplot

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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.

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.

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.

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