3-3 Measures of Relative Standing and Boxplots 127 In earlier sections of this chapter we described several statistics, including the mean, median, mode, range, and standard deviation. Some other statistics are defined using quartiles and percentiles, as in the following: Interquartile range (or IQR) = Q3 - Q1 Semi-interquartile range = Q3 - Q1 2 Midquartile = Q3 + Q1 2 10–90 percentile range = P90 - P10 5-Number Summary and Boxplot The values of the minimum, maximum and three quartiles 1Q1, Q2, Q32 are used for the 5-number summary and the construction of boxplot graphs. DEFINITION For a set of data, the 5-number summary consists of these five values: 1. Minimum 2. First quartile, Q1 3. Second quartile, Q2 (same as the median) 4. Third quartile, Q3 5. Maximum CP EXAMPLE 6 Finding a 5-Number Summary Use the “Space Mountain” wait times in Table 3-6 to find the 5-number summary. SOLUTION Because the “Space Mountain” wait times in Table 3-6 are sorted, it is easy to see that the minimum is 10 minutes and the maximum is 110 minutes. The value of the first quartile is Q1 = 25 minutes (from Example 4). The median is equal to Q2, and it is 35 minutes. Also, we can find that Q3 = 50 minutes by using the same procedure for finding P75 (as summarized in Figure 3-7). The 5-number summary is therefore 10, 25, 35, 50, and 110 (all in minutes). YOUR TURN. Find the 5-number summary in Exercise 31 “Radiation in Baby Teeth.” The values from the 5-number summary are used for the construction of a boxplot, defined as follows. DEFINITION A boxplot (or box-and-whisker diagram) is a graph of a data set that consists of a line extending from the minimum value to the maximum value, and a box with lines drawn at the first quartile Q1, the median, and the third quartile Q3. (See Figure 3-8 on the next page.) Procedure for Constructing a Boxplot 1. Find the 5-number summary (minimum value, Q1, Q2, Q3, maximum value). 2. Construct a line segment extending from the minimum data value to the maximum data value. 3. Construct a box (rectangle) extending from Q1 to Q3, and draw a line in the box at the value of Q2 (median).
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