92 CHAPTER 2 Descriptive Statistics Coefficient of Variation To compare variation in different data sets, you can use standard deviation when the data sets use the same units of measure and have means that are about the same. For data sets with different units of measure or different means, use the coefficient of variation. The coefficient of variation (CV ) of a data set describes the standard deviation as a percent of the mean. Population: CV = s m # 100% Sample: CV = s x # 100% DEFINITION Note that the coefficient of variation measures the variation of a data set relative to the mean of the data. Comparing Variation in Different Data Sets The table below shows the population heights (in inches) and weights (in pounds) of the members of a basketball team. Find the coefficient of variation for the heights and the weights. Then compare the results. Heights and Weights of a Basketball Team Heights 72 74 68 76 74 69 72 79 70 69 77 73 Weights 180 168 225 201 189 192 197 162 174 171 185 210 SOLUTION The mean height is m ≈ 72.8 inches with a standard deviation of s ≈ 3.3 inches. The coefficient of variation for the heights is CVheight = s m # 100% = 3.3 72.8 # 100% ≈ 4.5%. The mean weight is m ≈ 187.8 pounds with a standard deviation of s ≈ 17.7 pounds. The coefficient of variation for the weights is CVweight = s m # 100% = 17.7 187.8 # 100% ≈ 9.4%. Interpretation The weights (9.4%) are more variable than the heights (4.5%). TRY IT YOURSELF 10 Find the coefficient of variation for the office rental rates in Los Angeles (see Example 4) and for those in Dallas (see Try It Yourself 4). Then compare the results. Answer: Page A37 EXAMPLE 10
RkJQdWJsaXNoZXIy NjM5ODQ=