114 CHAPTER 3 Describing, Exploring, and Comparing Data DEFINITION The coefficient of variation (or CV) for a set of nonnegative sample or population data, expressed as a percent, describes the standard deviation relative to the mean, and is given by the following: Sample Population CV = s x # 100 CV = s m # 100 ROUND-OFF RULE FOR THE COEFFICIENT OF VARIATION Round the coefficient of variation to one decimal place (such as 25.3%). CP EXAMPLE 8 Wait Times for “Rock ‘n’ Roller Coaster” and “Tower of Terror” Table 3-5 includes measures of center and variation for the two data sets in Figure 3-2 on page 94. The measures of center fail to “see” the dramatic difference in variation between the two data sets. The table shows that the measure of center are identical, but the standard deviations of 28.8 and 12.1 are dramatically different. It would be a major error to make the comparison based on measures of center alone. TABLE 3-5 Comparison of Disney Wait Times (minutes) Mean Median Mode Midrange Standard Deviation Variance Rock ‘n’ Roller Coaster 57.3 55.0 45 62.5 28.8 831.8 Tower of Terror 57.3 55.0 45 62.5 12.1 146.8 It’s a good practice to compare two sample standard deviations only when the sample means are approximately the same. When comparing variation in samples or populations with very different means, it is better to use the coefficient of variation. Also use the coefficient of variation to compare variation from two samples or populations with different scales or units of values, such as the comparison of variation of heights of adult males and weights of adult males. EXAMPLE 9 Heights of Adult Males and Weights of Adult Males Use the data from Data Set 1 “Body Data” to compare the variation of heights (cm) of adult males and weights (kg) of adult males. For the heights of the males included in Data Set 1, x = 174.12 cm and s = 7.10 cm. For the weights of those same adult males, x = 85.54 kg and s = 17.65 kg. Note that we want to compare variation among heights (cm) and weights (kg), and we are working with different units of measure. SOLUTION We can directly compare the standard deviations if the same scales and units are used and the two means are approximately equal, but here we have different scales and different units of measurement, so we use the coefficients of variation:
RkJQdWJsaXNoZXIy NjM5ODQ=