CK-12 Probability and Statistics - Advanced

(Marvins-Underground-K-12) #1

2.2. Common Graphs and Data Plots http://www.ck12.org


discussions of these ideas, as well as statistics to quantify them, for a later chapter, but direction and strength are
easy to introduce in this example. The easiest way to describe these traits for this scatterplot is to think of the data
as a “cloud.” If you draw an ellipse around the data, the general trend is that the ellipse is rising from left to right.


Data that is oriented in this manner is said to have a positive linear association. That is, as one variable increases,
the other variable also increases. In this example, it is mostly true that country’s with higher paper recycling rates
have higher glass recycling rates. This is similar to a concept of slope in Algebra. Lines that rise in this direction
have a positive slope, and lines that trend downward from left to right have a negative slope. If the ellipse cloud
was trending down in this manner, we would say the data had a negative linear association. For example, we might
expect this type of relationship if we graphed a country’s glass recycling rate with the percentage of glass that ends
up in a landfill. As the recycling rate increases, the landfill percentage would have to decrease.


The ellipse cloud also gives us some information about the strength of the linear association. If there were a strong
linear relationship between glass and paper recycling rates, the cloud of data would be much longer than it is wide.
Long and narrow ellipses mean strong linear association, shorter and wider one’s show a weaker linear relationship.
In this example, there are some countries in which the glass and paper recycling rates do not seem to be related.

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