# Graphing: A Brief Review

Many of the concepts that economists study can be expressed with numbers – the price of bananas, the quantity of bananas sold, the cost of growing bananas, and so on. Often, these economic variables are related to one another. When the price of bananas rises, people buy fewer bananas. One way of expressing the relationships among variables is with graphs.

Graphs serve two purposes. First, when developing economic theories, graphs offer a way to visually express ideas that might be less clear if described with equations or words. Second, when analyzing economic data, graphs prove a way of finding how variables are in fact related in the world. Whether we are working with theory or with data, graphs provide a lens through which a recognizable forest emerges from a multitude of trees.

Numerical information can be expressed graphically in many ways, just as a thought can be expressed in words in many ways. A good writer chooses words that will make an argument clear, a description pleasing, or a scene dramatic. An effective economist chooses the type of graph that best suits the purpose at hand.

Economists use graphs to study the mathematical relationships among variables. There can be some pitfalls that can arise in the use of graphical methods.

Graphs of a single Variable:

The pie chart (a circle divided into sectors indicating the income) shows how total income in the United States is divided among the sources of income, including compensation of employees, corporate profits, and so on. A slice of the pie represents each source’s share of the total. The bar graph compares income for four countries. The height of each bar represents the average income in each country. The time series graph in panel traces the rising productivity in the US business sector over time. The height of the line shows output per hour in each year. You have probably seen similar graphs in newspaper and magazines.

Graphs of Two variables: The Coordinate System>

Although the these graphs are useful in showing how a variable changes over time or across individual, such graphs are limited in how much they can tell us. These graphs display information only a single variable. Economists are often concerned with the relationships between variables. Thus there is a need to display two variables on a single graph. The coordinate system makes this possible.

Suppose you want to examine the relationship between study time and grade point average. For each student in your class, you could record a pair of numbers: hours per week spent studying and grade point average. These numbers could then be placed in parentheses as an ordered pair and appear as a single point on the graph.

We can graph these ordered pairs on a two dimensional grid. The first number in each ordered pair, called he x-coordinate, tells us the horizontal location of the point. The second number called the y-coordinate tells us the vertical location of the point. The point with both an x-coordinate and a y- coordinate of zero is known as the origin. The two coordinates in the ordered pair tell us where the point is located in relation to the origin: x units to the right of the origin and y units above it.

Figure graphs grade point average against study time for Albert E., Alfred E., and their classmates. This type of graph is called a scatter plot because it plots scattered points. Looking at this graph we immediately notice that points farther to the right (indicating more study time) also tend to be higher (indicating a better grade point average),. Because study time and grade point average typically move in the same direction, we say that these two variables have a positive correlation. By contrast, if we were to graph party time and grades, because these variables typically move in opposite directions, we call this a negative correlating. In either case, the coordinate system makes the correlation between the two variables easy to see.

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