Section 3.3 Measures of Position 131 The IQR method for finding outliers In Examples 3.28 and 3.29, we determined the outlier just by looking at the data and finding an extreme value. In many cases, this is a good way to find outliers. There are some formal methods for finding outliers as well. The most frequently used method is the IQR method. The IQR Method for Finding Outliers Step 1: Find the first quartile, Q1, and the third quartile, Q3, of the data set. Step 2: Compute the interquartile range. IQR = Q3 − Q1 Step 3: Compute the outlier boundaries. These boundaries are the cutoff points for determining outliers. Lower outlier boundary = Q1 − 1.5 IQR Upper outlier boundary = Q3 + 1.5 IQR Step 4: Any data value that is less than the lower outlier boundary or greater than the upper outlier boundary is considered to be an outlier. EXAMPLE 3.30 Detecting outliers Use the IQR method to determine which values, if any, in the absence data in Table 3.11 are outliers. Solution Step 1: In Example 3.27, we computed the first and third quartiles: Q1 = 45 and Q3 = 59. Step 2: IQR = Q3 − Q1 = 59 − 45 = 14 Step 3: The outlier boundaries are: Lower outlier boundary = 45 − 1.5(14) = 24 Upper outlier boundary = 59 + 1.5(14) = 80 Step 4: There are no values in the data set less than the lower boundary of 24. There is one value, 100, that is greater than the upper boundary of 80. Thus there is one outlier, 100. Check Your Understanding 3. Table 3.12 presents the 2008 payrolls (in millions of dollars) for each of the 30 Major League Baseball teams. Table 3.12 2008 Payrolls for Major League Baseball Teams Team Payroll Team Payroll Team Payroll New York Yankees 209 St. Louis Cardinals 101 Texas Rangers 68 Detroit Tigers 139 Toronto Blue Jays 99 Baltimore Orioles 67 New York Mets 138 Philadelphia Phillies 98 Arizona Diamondbacks 66 Boston Red Sox 133 Houston Astros 89 Minnesota Twins 62 Chicago White Sox 121 Milwaukee Brewers 81 Kansas City Royals 58 Los Angeles Angels 119 Cleveland Indians 79 Washington Nationals 55 Chicago Cubs 119 San Francisco Giants 77 Pittsburgh Pirates 49 Los Angeles Dodgers 119 Cincinnati Reds 74 Oakland Athletics 48 Seattle Mariners 118 San Diego Padres 74 Tampa Bay Rays 44 Atlanta Braves 102 Colorado Rockies 69 Florida Marlins 22 Source: CBS Sports
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