Key Concepts
• Construction of scatter plots.
• Interpretation of scatter plot.
• Construct and interpret a scatter plot
Introduction:
A set of BIVARIATE DATA involves two variables. Since these are represented as ORDERED PAIRS,
You can graph bivariate data on a SCATTER PLOT.
A SCATTER PLOT is a graph with points plotted to show the relationship between two sets of data.
A CLUSTER is a set of closely grouped data.
![SCATTER PLOT](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-566-1024x837.png)
Data may cluster around a POINT or along a LINE.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-562-1024x845.png)
4.1.1 Construction of Scatter Plots
Example 1:
Mr. Jasper collected data from some of the students in grade 8 class.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-565-755x1024.png)
How can he determine whether there is a relationship between the hours spent studying and the test grade?
Solution:
Step 1: Label the axes. This will determine your x & y coordinates.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-563-1024x453.png)
Step 2: Convert the data into ordered pairs and plot each ordered pair on the graph.
Create a scatter plot for the data.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-564.png)
4.1.2 Interpretation of Scatter Plot
ASSOCIATION (CORRELATION) describes how sets of data are related.
- When both sets of data INCREASE together, it means POSITIVE ASSOCIATION. (CORRELATION)
![POSITIVE ASSOCIATION.](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-562-1024x845.png)
- When both sets of data DECREASE together, it means NEGATIVE ASSOCIATION. (CORRELATION)
![NEGATIVE ASSOCIATION.](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-567-1024x829.png)
- When there is NO RELATIONSHIP between the two data sets, it means NO ASSOCIATION. (CORRELATION)
![NO ASSOCIATION.](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-568-1024x922.png)
Example 2:
Susan asked 20 people if they would buy a new product she developed at each of several prices. She plotted her data in the scatter plot below, which shows how many of the 20 said “yes” at a given price. Describe the association between price and the number of buyers.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-569-881x1024.png)
What kind of association is shown?
What does this mean?
Solution:
Look at the way the data points are clustered.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-570-1024x530.png)
The scatter plot shows a negative association between price and buyers.
It means the number of buyers will decrease as the price of the product increases.
4.1.3 Construct and Interpret a Scatter Plot
Example 3:
A scientist gathers information about the eruptions of Old Faithful, a geyser in Yellowstone National Park. She uses the data to create a scatter plot. The data show the length of time between eruptions (interval) and how long the eruption lasts (duration).
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-571-1024x964.png)
![eruptions of Old Faithful](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-572.png)
Describe any clusters you see.
Describe any outliers you see.
Is there an association between the interval and the duration?
Solution:
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-573.png)
Exercise:
- A set of ______________________ involves two variables.
- A ________________ is a graph with points plotted to show the relationship between two sets of data.
- _______________ is a value much greater or much less than the others in a data set.
- The following table shows the height of some grade 8 boys and their fathers.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-647.png)
- Construct a scatter plot for the data.
- Does the scatter plot suggest a relationship between a boy’s height and his father’s height? Explain.
- Observe the following graph and describe the association between the number of customers and the amount of clothing sold.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-648.png)
- Roger constructs a scatter plot to show the data. What scales could he use for the x- and y-axes?
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-649.png)
- The table shows the racing times in minutes for the first two laps in a race. Complete the scatter plot.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-650.png)
- The following scatter plot represents the prices and number of books sold in a book store. Identify the cluster in the scatter plot and explain what it means.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-651.png)
- The table shows the monthly attendance in thousands at museums in one country over a 12-month period
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-652.png)
Complete the following scatter plot to represent the data.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-653.png)
Identify any outliers in the scatter plot.
- The plot shows the reading level and height of 16 students in a district. Describe the association and give a possible reason for it.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-654.png)
Concept Map:
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-577.png)
What have we learned:
• Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities.
• Describe patterns such as clustering, outliers, positive or negative association.
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