Example 37

EXAMPLE 37 IQR method for detecting outliers

Table 27 contains the value of exports by the United States to a sample of 12 countries around the world. Determine if there are any outliers in the country export data.

Table 3.98: Table 27 U.S. Exports

Country	U.S. exports ($ millions)
Italy	1.2
Saudi Arabia	1.7
India	1.9
France	2.8
Brazil	3.5
South Korea	3.8
United Kingdom	4.4
Germany	4.5
Japan	5.6
China	9.7
Mexico	20.3
Canada	26.3

FIGURE 41 Five-number summary.

Solution

The TI 1-Var Stats analysis provides the five-number summary shown in Figure 41.

Using these statistics, we calculate the IQR to be $Q 3 - Q 1 = 7.65 - 2.35 = 5.3$ . The quantity $1.5 (IQR) = 1.5 (5.3) = 7.95$ . We next find the two quantities $Q 1 - 1.5 (IQR)$ and $Q 3 + 1.5 (IQR)$ :

$\begin{array}{l} Q_{1} - 1.5 (IQR) = 2.35 - 7.95 & = - 5.6 \\ Q_{3} + 1.5 (IQR) = 7.65 + 7.95 & = 15.6 \end{array}$

Thus, for this data set, a data value would be an outlier if it were –5.6 or less or 15.6 or more. No data values are —5.6 or less. However, both Mexico (20.3) and Canada (26.3) have values greater than 15.6. Therefore, both the $20.3 million in exports to Mexico and the $26.3 in exports to Canada may be considered outliers, using the IQR method.

NOW YOU CAN DO

Exercises 11–12, 17–18, and 23–24.