Science, Tech, Math › Math How Bar Graphs Are Used to Display Data Share Flipboard Email Print A bar graph constructed from favorite foods mentioned by elementary school students. C.K.Taylor Math Statistics Statistics Tutorials Formulas Probability & Games Descriptive Statistics Inferential Statistics Applications Of Statistics Math Tutorials Geometry Arithmetic Pre Algebra & Algebra Exponential Decay Functions Worksheets By Grade Resources View More By Courtney Taylor Professor of Mathematics Ph.D., Mathematics, Purdue University M.S., Mathematics, Purdue University B.A., Mathematics, Physics, and Chemistry, Anderson University Courtney K. Taylor, Ph.D., is a professor of mathematics at Anderson University and the author of "An Introduction to Abstract Algebra." our editorial process Courtney Taylor Updated May 13, 2018 A bar graph is a way to visually represent qualitative data. Qualitative or categorical data occurs when the information concerns a trait or attribute and is not numerical. This kind of graph emphasizes the relative sizes of each of the categories being measured by using vertical or horizontal bars. Each trait corresponds to a different bar. The arrangement of the bars is by frequency. By looking at all of the bars, it is easy to tell at a glance which categories in a set of data dominate the others. The larger a category, the bigger that its bar will be. Big Bars or Small Bars? To construct a bar graph we must first list all the categories. Along with this, we denote how many members of the data set are in each of the categories. Arrange the categories in order of frequency. We do this because the category with the highest frequency will end up being represented by the largest bar, and the category with the lowest frequency will be represented by the smallest bar. For a bar graph with vertical bars, draw a vertical line with a numbered scale. The numbers on the scale will correspond to the height of the bars. The greatest number that we need on the scale is the category with the highest frequency. The bottom of the scale is typically zero, however, if the height of our bars would be too tall, then we can use a number greater than zero. We draw this bar and label the bottom of it with the title of the category. We then continue the above process for the next category and conclude when bars for all categories have been included. The bars should have a gap separating each of them from one another. An Example To see an example of a bar graph, suppose that we gather some data by surveying students at a local elementary school. We ask every one of the students to tell us what his or her favorite food is. Of 200 students, we find that 100 like pizza the best, 80 like cheeseburgers, and 20 have a favorite food of pasta. This means that the highest bar (of height 100) goes to the category of pizza. The next highest bar is 80 units high and corresponds to cheeseburgers. The third and final bar represents the students who like pasta the best and is only 20 units high. The resulting bar graph is depicted above. Notice that both the scale and categories are clearly marked and that all the bars are separated. At a glance, we can see that although three foods were mentioned, pizza and cheeseburgers are clearly more popular than pasta. Contrast With Pie Charts Bar graphs are similar to pie chart since they are both graphs that are used for qualitative data. In comparing pie charts and bar graphs, it is generally agreed that between these two kinds of graphs, bar graphs are superior. One reason for this is that it is much easier for the human eye to tell the difference between the heights of bars than wedges in a pie. If there are several categories to graph, then there can be a multitude of pie wedges that appear to be identical. With a bar graph, it is easier to compare heights a know which bar is higher. Histogram Bar graphs are sometimes confused with histograms, probably because they resemble each other. Histograms do indeed also use bars to graph data, but a histogram deals with quantitative data that is numerical rather than qualitative data, and of a different level of measurement.