Graphs and Graphing

A bar graph is used to picture the relationship between a relatively small number of objects, such as information listed in tabular form. Tables often represent mathematical relations, in that they consist of ordered pairs (listed in rows) for which the first and second elements of each pair (listed in separate columns) are related in a specific way. For example, a department store receipt is a relation defined by a table. It lists each item purchased together with its retail price. The first element of each ordered pair is the item, the second element is that item's purchase price. This type of relation lends itself well to the bar graph, because it contains information that is not strictly numeric, and because there are relatively few ordered pairs. In this example the prices are represented by points on the vertical axis, while the items purchased are represented by short line segments centered about the first few positive integers on the horizontal axis. To create the graph, the price of each item is located on the vertical axis, and a bar of that height is filled in directly above the location of the corresponding item on the horizontal axis. The advantage of the bar graph is that it allows immediate comparison of the relative purchase prices, including identification of the most expensive and least expensive items. It also provides a visual means of estimating the average cost of an item, and the total amount of money spent.