Graphing Tips and Tricks

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Dave Anderson: Hi. I'm Dave Anderson. Thanks for joining me for an adventure in economics. You've seen graphs before, unless you grew up in a cave, or maybe even if you did. This video will help you feel more comfortable working with graphs and get more information out of them.

Take a look at this graph over here. The axes are simply number lines that indicate the values of variables. Variables are measures that can take on more than one value. For example, the horizontal or x-axis on the bottom measures the number of salamanders the cave dwellers caught on a particular day. The vertical or y-axis on the left side measures the value of another variable, the number of fish caught on a particular day.

Each point on the graph represents two values, the number of salamanders and the number of fish caught on that day. We can label each point with a pair of numbers, the first one being the value of the variable measured on the horizontal axis and the second one being the value of the variable measured on the vertical axis.

This graph tells us that on day one, the cave dwellers caught one salamander and one fish. On day two, they caught two salamanders and four fish. And on day three, they caught four salamanders and two fish. A graph like this with points to indicate the values of two variables from observations in different situations, such as on different days or in different places or for different people, is called a scatter diagram.

The points on this graph show the relationship between two different types of variables, an independent variable and a dependent variable. The independent variable is the number of blackberry bushes in the area. This number changes due to things like droughts and forest fires.

But it is, for the purposes of this example, independent of the number of bears in the area. The number of bears in the area is the dependent variable, because its value depends on the independent variable. Bears like to eat blackberries. The points on this graph illustrate this relationship.

Looking at the white line drawn through these points, we can clearly see that as the number of blackberry bushes increases, the number of bears increases. When an increase in the independent variable causes an increase in the dependent variable, we say that the variables have a positive relationship.

This graph shows the number of fishers fishing in the pond and the average number of fish caught per fisher. If there is just one fisher, she has the whole pond to herself and she catches four fish. Looking at the white line drawn through all of these points, we can clearly see that is the number of fishers increases, there is more competition for the fish in the pond and the average number of fish caught per fisher decreases. When an increase in one variable causes a decrease in the other variable, we say that the variables have a negative relationship.

Now, consider the points on a graph with the number of cave paintings in the cave measured on the horizontal axis and the number of antelopes grazing in the forest on the vertical axis. If these variables are unrelated, an increase in the number of cave paintings won't cause a change in the number of antelopes grazing in the forest. So the line through these points will be horizontal, in this case showing us that there will be 30 antelopes grazing in the forest, regardless of the number of paintings in the cave.

We can better understand how changes in an independent variable affect the dependent variable, by looking at the slope of the line that depicts their relationship. The slope of a line between two points is found by dividing the rise in the line by the run. The rise is the change in the line's height found as the change in the y-axis variable. The run is the change from left to right found as the change in the x-axis variable.

In this graph, the rise is 6 and the run is 3. So the slope of the line between point A and point B is 6 over 3, or 2. In this, graph the rise is negative 2, because we go down two from point C to point D and the run is 4. So the slope of the line between point C and point D is negative 0.5.

A straight line has the same slope everywhere along the line. An upward sloping line has a positive slope. A downward sloping line has a negative slope. A flat line has a slope of 0. And a vertical line has a slope that is infinite or undefined.

The slope of a curved line changes as you move along the line. This graph shows how the total number of bear burgers sold by Cave Brothers Restaurant increased over time, which they measured with moons, as in the expression many moons ago. The slope of a curve at any point is the same as the slope of a straight line that touches the curve at that point.

We can see that the slope of a line touching this curve is positive, but decreases over time. The positive slope tells us that more burgers were sold every day. The decreasing slope tells us that daily sales, though positive, were getting smaller and smaller.

Now, consider this graph, which shows the relationship between the season and the number of tourists at Monmouth Cave. As winter approaches, fewer people visit the cave, with a minimal number in the dead of winter. And then, spring brings more visitors. The slope of this line starts out negative, because the number of tourists decreases in the winter.

The increase in the slope, going from a large negative number to a smaller negative number, tells us that the drop in visitors starts out large and then gets smaller. The slope is 0 at the minimum tourism level. And the slope is positive as spring approaches. The slope continues to increase when it becomes positive, showing that the increases in visitors get larger and larger.

The last graph that I want to show you is called the bar graph, because it uses bars of various lengths or heights to show the values of a dependent variable. This bar graph shows us, in a clear and concise manner, the number of pieces of firewood collected in one week by each cave dweller. This bar graph shows us the number of cave dwellers collected in one week by each bear.

They say a picture is worth a thousand words. The same is true for graphs. Get to know graphs and you will gain a tool that economists have found to be almost as useful as fire.