Scatter Plots – Concept and Explanation

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. 

Data may cluster around a POINT or along a LINE. 

4.1.1 Construction of Scatter Plots 

Example 1: 

Mr. Jasper collected data from some of the students in grade 8 class.  

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. 

Step 2:  Convert the data into ordered pairs and plot each ordered pair on the graph. 

Create a scatter plot for the data. 

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) 

• When both sets of data DECREASE together, it means NEGATIVE ASSOCIATION. (CORRELATION) 

• When there is NO RELATIONSHIP between the two data sets, it means NO ASSOCIATION. (CORRELATION) 

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. 

What kind of association is shown? 

What does this mean? 

Solution: 

Look at the way the data points are clustered.  

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). 

Describe any clusters you see. 

Describe any outliers you see. 

Is there an association between the interval and the duration? 

Solution: 

Exercise:

1. A set of ______________________ involves two variables.
2. A ________________ is a graph with points plotted to show the relationship between two sets of data.
3. _______________ is a value much greater or much less than the others in a data set.
4. The following table shows the height of some grade 8 boys and their fathers.

• 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.

• Roger constructs a scatter plot to show the data. What scales could he use for the x- and y-axes?

• The table shows the racing times in minutes for the first two laps in a race. Complete the scatter plot.

• 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.

• The table shows the monthly attendance in thousands at museums in one country over a 12-month period

Complete the following scatter plot to represent the data.

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.

Concept Map:

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.