1.1.3 Scatter Plots

One way to display the general relationship between two variables is to make a scatter plot, that is, a graph in a rectangular coordinate system of all the pairs of data. In Figure 1 we show a computer-generated scatter plot of the fifty-one data points in Table 1. Making such a graph is easy if there are not too many points. For this many points, it would be tedious to make the plot by hand. [Help for making scatter plots with your graphing calculator or a computer.]

For each state, the pair of numbers consisting of a spending amount and a graduation rate is represented by one point in the plane. State spending is plotted on the horizontal axis, and graduation rate is plotted on the vertical axis. For example, the pair representing New York is (`\$`10,039, 61.4%). When making a scatter plot, it really does not matter which variable is plotted on which axis. If we suspect that one variable is dependent on the other, however, we usually plot the dependent variable on the vertical axis.

Activity 3

1. Find the plotted point you think represents New York in Figure 1.

2. Are you surprised by the point that lies to the right of and far above the others? Which state does that point represent?

3. Study the scatter plot carefully. Does there appear to be any relationship between state spending and the graduation rate?

4. Which display do you find easier to interpret, the table or the graph?

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Checkpoint 2

Activity 4

Tables 2, 3, and 4 show the total numbers of rebounds, assists, personal fouls committed, and points scored by individual basketball players on three professional basketball teams during the 2004-05 season. Study the Fouls and Points columns in Tables 2, 3, and 4, and think about whether there is a relationship between the number of personal fouls that a basketball player commits in a season of play and the number of points he scores. In the scatter plot shown in Figure 2, we have plotted (for the three teams combined) personal fouls on the horizontal axis and points scored on the vertical axis.

1. What is the general shape of the plot in Figure 2?

2. How strong is the relationship between these variables? How well could you predict the points scored by a player committing 75 personal fouls?

3. In general, if you were given a value for one variable, how confident would you be in predicting a value for the other variable?

4. Does a change in one variable cause the other to change, or is this a situation where they simply change together as the result of some underlying factor?

5. Would you expect the coach to encourage his players to commit lots of fouls in order to be sure of scoring many points? If not, what underlying factors could be influencing both of our variables?

Note 3 – Data source

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Contents for Chapter 1