Lesson 7
Observing More Patterns in Scatter Plots
Let's look for other patterns in data.
7.1: Notice and Wonder: Nonlinear Scatter Plot
What do you notice? What do you wonder?
![A scatterplot.](https://cms-im.s3.amazonaws.com/Ftdxj1FZER3Sk3fZyjhAc43v?response-content-disposition=inline%3B%20filename%3D%228-8.6AScatter.pdf-15.png%22%3B%20filename%2A%3DUTF-8%27%278-8.6AScatter.pdf-15.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T040835Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6cb62ba486f409585fae62acedc0c697e9caca3d3dc7b2ff73cf77382069ca9e)
7.2: Scatter Plot City
Your teacher will give you a set of cards. Each card shows a scatter plot.
- Sort the cards into categories and describe each category.
- Explain the reasoning behind your categories to your partner. Listen to your partner’s reasoning for their categories.
- Sort the cards into two categories: positive associations and negative associations. Compare your sorting with your partner’s and discuss any disagreements.
- Sort the cards into two categories: linear associations and non-linear associations. Compare your sorting with your partner’s and discuss any disagreements.
7.3: Clustering
How are these scatter plots alike? How are they different?
![Four scatterplots.](https://cms-im.s3.amazonaws.com/1EHTyhPeDgZyanFGdRBa7w6e?response-content-disposition=inline%3B%20filename%3D%228.6.B5.Image.02%20%25281%2529.png%22%3B%20filename%2A%3DUTF-8%27%278.6.B5.Image.02%2520%25281%2529.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T040835Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=83281c731e1b293b95ac2fcd736d1888d74c17eb8037d91e29ff470042c03b17)
Summary
Sometimes a scatter plot shows an association that is not linear:
![Scatterplot, x, 0 to 12 by 3, y, 0 to 30 by 6. Points begin near 1 comma 24 and trend down and to the right until about 6 comma 2, and then trend up and to the right to about 11 comma 25.](https://cms-im.s3.amazonaws.com/nPSPmjnWYa54K813ddnacPK7?response-content-disposition=inline%3B%20filename%3D%228-8.6.B5.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%278-8.6.B5.Image.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T040835Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=99cfcdb258ca6d5351284211bea8ebe83323eeaf4a483e7e9cc5c375e86779b2)
We call such an association a non-linear association. In later grades, you will study functions that can be models for non-linear associations.
Sometimes in a scatter plot we can see separate groups of points.
![A scatterplot with two groups of points.](https://cms-im.s3.amazonaws.com/AmF81ec2xcXxknhwbgVbC1oE?response-content-disposition=inline%3B%20filename%3D%228-8.6.B5.Image.05.png%22%3B%20filename%2A%3DUTF-8%27%278-8.6.B5.Image.05.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T040835Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1b8f668c0d038eac7f0f382885ba6945b20af7f69c157a8219c1bc612fb8e18a)
We call these groups clusters.
Glossary Entries
- negative association
A negative association is a relationship between two quantities where one tends to decrease as the other increases. In a scatter plot, the data points tend to cluster around a line with negative slope.
Different stores across the country sell a book for different prices.
The scatter plot shows that there is a negative association between the the price of the book in dollars and the number of books sold at that price.
- outlier
An outlier is a data value that is far from the other values in the data set.
Here is a scatter plot that shows lengths and widths of 20 different left feet. The foot whose length is 24.5 cm and width is 7.8 cm is an outlier.
- positive association
A positive association is a relationship between two quantities where one tends to increase as the other increases. In a scatter plot, the data points tend to cluster around a line with positive slope.
The relationship between height and weight for 25 dogs is shown in the scatter plot. There is a positive association between dog height and dog weight.