Statistics and Probability 8.SP.A.1
1. 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, linear association, and nonlinear association.
Many esteemed statisticians have discovered that there appears to be a strange link between Justin Bieber's singing and the population of capuchin monkeys in Argentina. Whenever Bieber hits a high note, there is a spurt in the number of baby capuchins. The higher the frequency of the note, the more baby monkeys are born.
We could list all the different frequencies of Bieber's voice and the number of baby monkeys that were born at those high notes. But that's just a list of numbers—and we most people will probably give up on making sense of it long before they can be convinced.
A better way to see whether there's a relationship between this bivariate data (that simply means two different sets of numbers) would be to make a scatter plot.
Along the bottom, we'll list the frequencies of Bieber's high notes while in concert. On the side, we'll list the number of baby monkeys that were born at those frequencies. Then, we'll put a dot on the graph corresponding to the note and number of monkey births. Turns out, our graph looks like this:
What exactly could we deduce from this data? Well, there certainly seems to be a relationship between high notes and the birth of baby capuchins; the higher the notes, the more babies.
Students should understand scatter plots as ways to communicate relationships between two variables. The more linear the graph, the stronger the correlation. Students should also be able to identify and define outliers and clusters and give possible reasons for their existence. For instance, holding out a shaky high note might result in a few clusters around that particular frequency, not to mention a few fans clustering toward the exit.
Students should also be able to interpret scatter plots as having linear or nonlinear associations, and discern whether these associations are positive or negative. They can think of positive and negative as describing the "slope" of the data. If there's a positive association, both variables increase together. If there's a negative slope, one increases while the other decreases. We don't mean "positive" or "negative" for the capuchin monkey population. Let PETA take that one on.