## Graph and Analyze Data

There are many situations in which a numerical value is associated with different objects or categories, such as counting the number of students in the various classes at a school.

One way of representing such data is by expressing the associated numerical values with tally marks. To make the marks easier to count, they are organized in groups of five, each group having four vertical marks followed by a slash mark diagonally across them.

One advantage of this kind of representation of numbers is that it allows a number to be replaced by a greater one simply by adding more marks. Also, the size of the symbol corresponds to the size of the number being represented. The fact that 81 is much greater than 29 is vividly clear if one uses tally marks in place of positional notation.

Another way of representing data is by using a bar graph. Here the objects or categories are listed along the horizontal axis and the associated numerical value is indicated by the length of a bar above the category. A vertical axis provides a scale for converting the length of the bar into a number.

For example, the fact that John counted 70 cars, Mary counted 60 cars, and Jim counted 45 cars can be represented by the following bar graph.

A line plot is closely related to a bar graph. Line plots tend to be used when the data are categorical. A mark, X, is used to represent each object corresponding to a particular category. If a bowl of fruit contains 3 apples, 5 plums, and 2 oranges, then the corresponding line plot takes the following form.

**Teaching Model 6.7:** Read Graphs With Ordered Pairs