48 CHAPTER 2 Exploring Data with Tables and Graphs TABLE 2-3 Causes of Fatal Plane Crashes Cause Frequency Pilot Error 640 Mechanical 195 Sabotage 95 Weather 63 Other 111 YOUR TURN. Do Exercise 27 “Software Piracy.” Now let’s shift gears (pun intended) and compare commute times of two different cities. Table 2-5 shows the relative frequency distributions for 1000 commute times in New York and Boise from Data Set 31. Because of the different sizes of these two cities, we might expect the commute times to be very different. By comparing the relative frequencies in Table 2-5, we see that there are major differences. The Boise commute times appear to be lower than the New York commute times. (See that for Boise, the lowest two classes have 75.8% of all commute times, compared to only 28.9% for New York.) This is not surprising given the relative size and population density of these cities. CP EXAMPLE 3 Comparing Daily Commute Time in New York, NY and Boise, ID Go Figure 14: The number of different shapes of human noses, from a study by Abrahim Tamir that was published in the Journal of Craniofacial Surgery. Relative Frequency Distribution A variation of the basic frequency distribution is a relative frequency distribution or percentage frequency distribution, in which each class frequency is replaced by a relative frequency (or proportion) or a percentage. In this text we use the term “relative frequency distribution” whether we use relative frequencies or percentages. Relative frequencies and percentages are calculated as follows. Relative frequency for a class = frequency for a class sum of all frequencies Percentage for a class = frequency for a class sum of all frequencies * 100, Table 2-4 is an example of a relative frequency distribution. It is a variation of Table 2-2 in which each class frequency is replaced by the corresponding percentage value. The sum of the frequencies in Table 2-2 is 50, so the percentages for the classes can be found by dividing each class frequency by 50, and then multiplying by 100%. The first class of Table 2-2 has a frequency of 6, so divide 6 by 50 to get 0.12, and then multiply by 100% to get 12%. The sum of the percentages should be 100%, with a small discrepancy allowed for rounding errors, so a sum such as 99% or 101% is usually acceptable. The sum of the percentages in Table 2-4 is 100%. The sum of the percentages in a relative frequency distribution must be very close to 100% (with a little wiggle room for rounding errors). Comparisons Example 3 illustrates this principle: Combining two or more relative frequency distributions in one table makes comparisons of different data sets much easier. TABLE 2-4 Relative Frequency Distribution of Daily Commute Times in Los Angeles Daily Commute Time in Los Angeles (minutes) Relative Frequency 0–14 12% 15–29 36% 30–44 28% 45–59 10% 60–74 10% 75–89 2% 90–104 2%
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