132 Chapter 3 Numerical Summaries of Data a. Construct the five-number summary. b. Find the IQR. c. Find the upper and lower outlier boundaries. d. Which values, if any, are outliers? Answers are on page 139. Objective 6 Construct boxplots to visualize the five-number summary and outliers Explain It Again Another name for boxplots: Boxplots are sometimes called box-and-whisker diagrams. Boxplots A boxplot is a graph that presents the five-number summary along with some additional information about a data set. There are several kinds of boxplots. The one we describe here is sometimes called a modified boxplot. Procedure for Constructing a Boxplot Step 1: Compute the first quartile, the median, and the third quartile. Step 2: Draw vertical lines at the first quartile, the median, and the third quartile. Draw horizontal lines between the first and third quartiles to complete the box. Step 3: Compute the lower and upper outlier boundaries. Step 4: Find the largest data value that is less than the upper outlier boundary. Draw a horizontal line from the third quartile to this value. This horizontal line is called a whisker. Step 5: Find the smallest data value that is greater than the lower outlier boundary. Draw a horizontal line (whisker) from the first quartile to this value. Step 6: Determine which values, if any, are outliers. Plot each outlier separately. EXAMPLE 3.31 Constructing a boxplot Construct a boxplot for the absence data in Table 3.11. Solution Step 1: In Example 3.27, we computed the median to be 51 and the first and third quartiles to be Q1 = 45 and Q3 = 59. Step 2: We draw vertical lines at 45, 51, and 59, then horizontal lines to complete the box, as follows: 40 50 60 70 80 90 100 Number of Absences Step 3: We compute the outlier boundaries as shown in Example 3.30: Lower outlier boundary = 45 − 1.5(14) = 24 Upper outlier boundary = 59 + 1.5(14) = 80 Step 4: The largest data value that is less than the upper boundary is 77. We draw a horizontal line from 59 up to 77, as follows: 40 50 60 70 80 90 100 Number of Absences
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