Exam Scores. The exam scores for the students in an introductory statistics class are as follows.

88 82 89 70 85 63 100 86 67 39 90 96 76 34 81 64 75 84 89 96

a. Group these exam scores, using the classes 30–39, 40–49, 50–59, 60–69, 70–79, 80–89, and 90–100.

b. What are the widths of the classes?

c. If you wanted all the classes to have the same width, what classes would you use?

Choosing the Classes. One way that we can choose the classes to be used for grouping a quantitative data set is to first decide on the

(approximate) number of classes. From that decision, we can then determine a class width and, subsequently, the classes themselves.

Several methods can be used to decide on the number of classes. One method is to use the following guidelines, based on the number of observations:

Number of Number of observations classes 25 or fewer 5–6 25–50 7–14 Over 50 15–20 With the preceding guidelines in mind, we can use the following stepby-step procedure for choosing the classes.

Step 1 Decide on the (approximate) number of classes.

Step 2 Calculate an approximate class width as Maximun observation − Minimum observation Number of classes and use the result to decide on a convenient class width.

Step 3 Choose a number for the lower limit (or cutpoint) of the first class, noting that it must be less than or equal to the minimum observation.

Step 4 Obtain the other lower class limits (or cutpoints) by successively adding the class width chosen in Step 2.

Step 5 Use the results of Step 4 to specify all of the classes.