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Describing Scatterplots
Common Core: 8.SP.1

Describing Scatterplots

Author: Ryan Backman
Description:

Identify the direction and strength of a scatterplot.

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Tutorial

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Hi. This tutorial covers describing scatter plots. So when data's presented using a scatter plot, it is important to be able to describe the following characteristics of the relationship. And the relationship here we're talking about is the relationship between x and y. So the three things are direction, strength, and form.

And we'll address each of these and we'll look at a couple examples of each. So let's start with direction. Direction measures how the y values of an association generally change as the x values increase. And really, we have three different directions. We are positive, negative, and then really no association.

So if the x values increase-- excuse me-- if the y values increase as the x values increase, the direction is positive. And we'll look at a scatter plot that has a positive association in a minute here. If the y values decrease as the x values increase, the direction is negative. Then, if the points appear as a cloud or a-- or as a horizontal line, then we say there is no association, or very little association.

So let's take a look at a couple different scatter plots and look at the differences in direction. So let's start with the scatter plot here. So let's say that we had a scatter plot that looks kind of something like that. So remember that this is your x-axis and this is your y-axis. So as your x values increase, our y values are also tending to increase. So what we say here is that this is a positive association.

Now, if we want a negative association, as our x values increase, our y values will need to decrease. So usually, we'll start them up high here. We just have the first quadrant, but this can be done on any-- since now our y values are decreasing-- so the y values decrease as the x values increase-- this is a negative association. So this is negative.

And then, if we look at a distribution with no association, they're just going to appear as a cloud of points. So there's no real tendency for the y's to increase or decrease as the x's-- so here we would just say there's no association, or no direction here. So those are the big differences. Positive-- as x's increase, y increase. For negative-- as x's increase, y's decrease. And for no association, it's just a cloud of points.

Also, if our points were clustered around a horizontal line, that would also be a case of no association. OK, let's look at the next one called strength. So now, strength measures how close an association can be modeled using a curve-- a curve or a line, really. So we're going to look at really three different strengths. We'll start with a strong association.

We'll just assume that these can be modeled with a straight line. A strong association is going to be an association where your dots are really clustered around some line. We could also have some sort of curve. If they're really clustered around a curve, we'd also say that that would have a strong association. This is also a positive association, so we would say that this here is strong positive.

Now, if we look at maybe a moderate association, a moderate association-- you're still going to see an association being positive or negative, but there's going to be less of a tight cluster right around the line or the curve. So we'll say that this one is moderate. You could also have a moderate negative association, if they were-- if the y values were decreasing.

And then we'll also look at weak. So weak-- again, you're going to see some sort of association, but in this case, you're going to see a lot-- that clusters going not going to be as tight as in here, so this-- we would call it weak association. We could still see that slight positive association, but this one is pretty weak.

So that covers strength. So we've looked at direction and strength, and the last thing usually that we want to comment on is form. And form is really whether an association appears linear or nonlinear. And then also, clusters and outliers can be addressed when describing the form.

So let's start with a linear association. Most of the ones that I've showed so far have been pretty linear. Let's do a negative one. So if they really cluster around a pretty straight line, we would said this would be linear. So this would be probably a pretty strong, either strong or moderate negative linear association.

And then, if we look at something that's nonlinear, you might see it looking more like this, where we can see that there seems to be more of a curve. A curve would be a better fit for this data set. So I would say that this one is nonlinear. Like I said, you can also talk about clusters and outliers.

So this association might have an outlier down here. So you could talk about it an outlier when you're addressing the form. Maybe you have a big cluster of points here and an outlier way down here. You can talk about that cluster. But those are both two other things you can talk about, in terms of form.

So the big key things in this tutorial were the direction of an association-- either positive, negative, or none-- the strength of an association-- strong, moderate, or weak-- and then the form of an association-- either linear or nonlinear. So that has been the tutorial on describing scatter plots. Thanks for watching.

Terms to Know
Direction

The way one variable responds to an increase in the other. With a negative association, an increase in one variable is associated with a decrease in the other, whereas with a positive association, an increase in one variable is associated with an increase in the other.

Form

The overall shape of the data points. The form may be linear or nonlinear, or there may not be any form at all to the points, if they form a "cloud."

Strength

The closeness of the points to the indicated form. Points that are strongly linear will all fall on or near a straight line.