Displaying Data Visually
'Graphing' often is taken to mean lines on a coordinate grid, but there are many ways of displaying data in a visual format. In this lesson, students use their understanding of angle measure, area, fractions and probability to create a variety of graphs to represent various situations. Here is some sample data, in the form of a puzzle, and graphs similar to the ones the students produce in class.
72 students voted in an election:
In a circle graph, the 360 degrees must be divided evenly among the 72 votes, so each vote would be represented by 5 degrees.
In a bar graph, the height of each column is the number of votes received.
In both graphs, it is easy to see who won the election, and the relative positions of the other candidates. That's the purpose of a graph - to make data easily understood at a glance.
Another kind of graph is the rectangular area graph. For this set of data, here's how it would look.
In this graph, and the circle graph, it's easy to see that Sam and Barb together received half of the votes.
Sometimes data doesn't fit neatly into single categories like votes do. For instance, if we survey a group of students about sports, we might find that some students like more than one sport, so we have to have categories that reflect all the possible choices and preferences. Here's a set of data about a survey of sports preferences:
We could construct a circle graph, bar graph, or rectangle area graph to show the various results. Another possibility is a Venn diagram:
In the Venn diagram, it's easier to see how many students like each sport - for example, of the 30 students surveyed, 18 students like soccer, 16 like baseball, and 17 like basketball
The main thing to remember is that these graphs are visual displays of data. Our purpose is to make data more easily understood and interpreted so we can make decisions or find patterns that will help us in making decisions. Periodicals, newspapers and advertising all make ample use of graphs and visual displays of data. Take time with your child to examine some of those examples carefully. Talk about why the writers may have chosen a certain type of graph or how the graph they use might sway someone's opinion about the information. Be on the lookout for how graphs might be used in misleading ways so that the writer's point might seem more strongly supported.