Section 2.2 Frequency Distributions and Their Graphs 51 Requirements for Choosing Classes • Every observation must fall into one of the classes. • The classes must not overlap. • The classes must be of equal width. • There must be no gaps between classes. Even if there are no observations in a class, it must be included in the frequency distribution. The following procedure will produce a frequency distribution whose classes meet these requirements. Procedure for Constructing a Frequency Distribution for Quantitative Data Step 1: Choose a class width. Step 2: Choose a lower class limit for the first class. This should be a convenient number that is slightly less than the minimum data value. Step 3: Compute the lower limit for the second class by adding the class width to the lower limit for the first class: Lower limit for second class = Lower limit for first class + Class width Step 4: Compute the lower limits for each of the remaining classes, by adding the class width to the lower limit of the preceding class. Stop when the largest data value is included in a class. Step 5: Count the number of observations in each class, and construct the frequency distribution. EXAMPLE 2.10 Constructing a frequency distribution Construct a frequency distribution for the data in Table 2.7, using a class width of 1.50. Solution Step 1: The class width is given to be 1.50. Step 2: The smallest value in the data is 0.25. A convenient number that is smaller than 0.25 is 0.00. We will choose 0.00 to be the lower limit for the first class. Step 3: The lower class limit for the second class is 0.00 + 1.50 = 1.50. Step 4: Continuing, the lower limits for the remaining classes are 1.50 + 1.50 = 3.00 3.00 + 1.50 = 4.50 4.50 + 1.50 = 6.00 6.00 + 1.50 = 7.50 Since the largest data value is 6.64, every data value is now contained in a class. Step 5: We count the number of observations in each class to obtain the following frequency distribution. Frequency Distribution for Particulate Data Using a Class Width of 1.5 Class Frequency 0.00–1.49 28 1.50–2.99 18 3.00–4.49 15 4.50–5.99 2 6.00–7.49 2
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