SECTION 2.5 Measures of Position 105 1. The minimum entry 2. The first quartile Q1 3. The median Q2 4. The third quartile Q3 5. The maximum entry These five numbers are called the five-number summary of the data set. Drawing a Box-and-Whisker Plot 1. Find the five-number summary of the data set. 2. Construct a horizontal scale that spans the range of the data. 3. Plot the five numbers above the horizontal scale. 4. Draw a box above the horizontal scale from Q1 to Q3 and draw a vertical line segment in the box at Q2. 5. Draw whiskers from the box to the minimum and maximum entries. Minimum entry Maximum entry Whisker Whisker Q1 Q3 Median, Q2 Box GUIDELINES Drawing a Box-and-Whisker Plot Draw a box-and-whisker plot that represents the data set in Example 2. What do you observe? SOLUTION Here is the five-number summary of the data set. Minimum = 19 Q1 = 47 Q2 = 55 Q3 = 58.5 Maximum = 61 Using these five numbers, you can construct the box-and-whisker plot shown. 15 20 25 30 35 40 45 50 55 60 65 19 47 55 58.5 61 Tuition and Fees Interpretation The box represents about half of the data, which means about 50% of the data entries are between 47 and 58.5. The left whisker represents about one quarter of the data, so about 25% of the data entries are less than 47. The right whisker represents about one quarter of the data, so about 25% of the data entries are greater than 58.5. Also, the length of the left whisker is much longer than the right one. This indicates that the data set has a possible outlier to the left. (You already know from Example 3 that the data entry of 19 is an outlier). TRY IT YOURSELF 4 Draw a box-and-whisker plot that represents the points scored by the 55 winning teams listed on page 39. What do you observe? Answer: Page A37 You can use a box-and-whisker plot to determine the shape of a distribution. Notice that the box-and-whisker plot in Example 4 represents a distribution that is skewed left. See Minitab and TI-84 Plus steps on pages 124 and 125. EXAMPLE 4 Picturing the World From 1970 through 2019, there were 2939 fatalities in the United States attributed to lightning strikes. The box-and-whisker plot summarizes the fatalities for each of these years. (Source: National Weather Service) 10 30 50 70 90 110 130 16 38 51.5 74 124 Lightning Fatalities Fatalities per year from 1970 through 2019 About how many fatalities are represented by the right whisker? There were 20 lightning fatalities in 2019. Into what quartile does this number of fatalities fall? Study Tip For data sets that have outliers, you can represent them graphically using a modified box-and-whisker plot. A modified box-and-whisker plot is a box-and-whisker plot that uses symbols (such as an asterisk or a point) to indicate outliers. The horizontal line of a modified box-and-whisker plot extends as far as the minimum data entry that is not an outlier and the maximum data entry that is not an outlier. For instance, on pages 124 and 125, Minitab and the TI-84 Plus were used to draw modified box-and-whisker plots that represent the data set in Example 2. Compare these results with the one in Example 4.
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