12.2 Frequency Distributions and Statistical Graphs 773 The modal class of a frequency distribution is the class with the greatest frequency. In Example 2, the modal class is 50–94. A frequency distribution may have more than one modal class. The midpoint of a class, also called the class mark, is determined by adding the lower and upper class limits and dividing the sum by 2. The midpoint of the first class, and also the class mark of the first class, in Example 2 is 50 94 2 144 2 72 + = = The midpoint of the second class in Example 2 is 95 139 2 234 2 117 + = = Note that the difference between successive class marks, 117–72, is the class width 45. The class mark of the second class can therefore be obtained by adding the class width, 45, to the class mark of the first class, 72. The sum is 72 45 117. + = Note that 117 checks with the class mark obtained by adding the lower class limit and the upper class limit of the second class and dividing the sum by 2. Since the highest value in the data is 500, there is no need to go any further. Note that each two consecutive lower class limits differ by 45, as do each two consecutive upper class limits. There are 21 pieces of data in the 50–94 class, 5 in the 95–139 class, 2 in the 140–184 class, 1 in the 185–229 class, 0 in the 230–274 class, 0 in the 275–319 class, 0 in the 320–364 class, 0 in the 365–409 class, 0 in the 410–454 class, 0 in the 455–499 class, and 1 in the 500–544 class. The complete frequency distribution of the 11 classes is given below. The number of novels totals 30, so we have included each piece of data. Now try Exercise 13 Copies Sold (millions) Number of Novels 50 – 94 21 95 –139 5 140 – 184 2 185–229 1 230 –274 0 275–319 0 320–364 0 365 – 409 0 410 – 454 0 455 – 499 0 500 –544 1 30 7 Example 3 A Frequency Distribution of Family Income The following set of data represents the family income (in thousands of dollars, rounded to the nearest hundred) of 15 randomly selected families. 46.5 31.8 45.8 44.7 40.9 65.2 52.4 44.6 53.7 48.8 35.5 40.3 39.8 56.3 50.7 Construct a frequency distribution with a first class of 31.5–37.6.
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