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# Scatterplots

### Written by tutor Sarah C.

Scatterplots are special graphs showing the relationship, or correlation, between two different variables. Scatterplots are very similar to line graphs, except the data points shown are not necessarily spaced consistently and are not connected by a line. Consider the scatterplot shown below. What does it tell us?

This scatterplot shows the relationship between two variables, or factors: height and shoe size. There is not a perfect relationship between the two variables, which means we are unable to predict with certainty a person’s shoe size from simply knowing his or her weight. Let’s consider a specific portion of the scatterplot: heights that related to size 5 shoes. Individuals of three different heights (54, 56, and 57 inches) each wear size 5 shoes. If we look even closer, we can see that second person with a height of 57 inches wears size 6 shoes instead of size 5 shoes. This highlights, again our inability to use a scatterplot to form a definite prediction for the value of one variable based on the value of another.

So, if we cannot use scatterplots to predict specific outcome values, what is the benefit of using a scatterplot? Let’s look a little bit closer at the entire scatterplot. We have already discussed that a range of heights are related to wearing size 5 shoes. Does this hold true in all sizes? Look closely at shoe sizes 6, 7.5, and 8. In all shoe sizes, we see that shoe size is related to a variation in height.

Now, let’s broaden our focus to look at the entire scatterplot. Do you see any trends? Is there an overall relationship between height and shoe size? Yes! When we look at the entire graph, we can see that as height increases, shoe size generally increases as well. Does this information fit with your existing knowledge of height and shoe size? Sure it does!

By simply looking at one example scatterplot, we have learned that scatterplots can help us identify the relationship between two variables.

## Scatterplots Practice Quiz

True or false: Scatterplots allow you to accurately predict the value of one variable from another.

A. True
B. False
The correct answer here would be B, false! Because the relationship between the two variables is not consistent, scatterplots do not allow you to predict the exact value of one variable from a given value of another variable. Scatterplots do, however, allow you to see trends and hypothesize an approximate prediction of one variable based on the other.

True or false: The points on a scatterplot should be connected by lines.

A. True
B. False
The correct answer here would be B, false! We can only use lines to connect data points if we can predict all of the values between the data points. Since the relationship between variables in a scatterplot is not consistent, we cannot connect the points.