Imagine that a line on a Cartesian graph is approximately the distance y in feet a person walks in x hours. What does the slope of this line represent? How is this graph useful? Provide another example for your colleagues to explain. The slope of the line represents the speed of the person in feet per hour. This graph is useful because it provides a visual representation of the continuous motion of the person walking, something that could not provided by something like a bar graph. In a bar graph, the sheer number of columns and their shape makes representation of a temporal action cumbersome, whereas in a line graph, the information is represented fluidly, as it is reality. (See Figure 1 for another example.) What is the difference between a scatterplot and a line graph? Provide an example of each. Does one seem better than the other? In what ways is it better? A scatter plot consists of several data points placed on a Cartesian graph that are not connected to each other, where the data is shown as a collection of points. A line graph is an extension of the scatter plot in which the data is connected by straight segments of lines. A scatter plot might be used to analyze the relationship between achievement test scores and income (Figure 2), while a line graph might be used to analyze the distance traveled by a car in minutes (Figure 3). For certain purposes, especially those that involve relating two variables that related by some kind of formula, a line graph is better because it shows the definitive relationship between the two variables, a relationship that, due to the formulaic nature of the relationship, will not change. Scatter plots are best used for other relationships.
Figure 1. Cost of an object (y) and the Year (x) (http://www.westegg.com/inflation/)
Figure 2. Test Scores (y) and Income (x) (Hypothetical)
Figure 3. Distance traveled by a car in meters (y) and Time in minutes (x) (Hypothetical)