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Lesson 1.8 %u2022 Summarizing Quantitative Data: Boxplots and Outliers 87 Lesson 1.8 W H AT D I D Y O U L E A R N ? LEARNING TARGET EXAMPLE EXERCISES Use the 1.5 %u00d7 IQR rule to identify outliers. p. 80 7%u201310 Make and interpret boxplots of quantitative data. p. 83 11%u201314 Compare distributions of quantitative data with boxplots. p. 84 15%u201318 Building Concepts and Skills 1. True/False: The 1.5 %u00d7 IQR rule says that an outlier is any data value that is more than 1.5 %u00d7 IQRabove or below the median. 2. Give three reasons why it is important to identify outliers in a distribution of quantitative data. 3. What are the five values in the five-number summary? 4. In a boxplot, the width of the box is the . 5. True/False: When there are outliers, the whiskers in a boxplot extend to the lower/upper cutoff values for outliers. 6. What important information about the shape of a distribution could a boxplot hide? Mastering Concepts and Skills 7. Unusual heart rate Here are the resting heart rates (in beats per minute) of 26 ninth-grade biology students. Identify any outliers in the distribution. 61 48 77 81 78 75 70 77 70 76 86 55 65 60 63 79 62 71 72 74 74 64 66 71 66 68 8. Photo bytes How much storage space do digital photos use? Here are the file sizes (to the nearest tenth of a megabyte) for 18 randomly selected photos in Azucena%u2019s cloud storage. Identify any outliers in the distribution. 2.4 2.7 1.6 1.3 6.2 1.3 5.6 1.1 2.2 1.9 2.1 4.4 4.7 3.0 1.9 2.5 7.5 5.0 9. Pizza with outliers The dotplot shows the number of calories per serving for 16 brands of frozen cheese pizza. 102 Identify any outliers in the distribution. 260 280 300 320Calories340 360 380 40010. July heat The dotplot displays the high temperature readings in degrees Fahrenheit for Phoenix, Arizona, for each day in July in a recent year. 103 Identify any outliers in the distribution. Daily high temperature (%u02daF)85 90 95 100 105 110 115 11. Daily texts According to blogger Kenneth Burke, adults ages 18 to 24 send an average of 64 texts per day. 104 Dr. Williams suspected that this value was exaggerated, and collected data from a class of Introductory Statistics students on the number of texts they had sent in the past 24 hours. Here are the data:0 7 1 29 25 8 5 1 25 98 9 0268 118 72 0 92 52 14 3 3 44 5 42(a) Make a boxplot to display the data. (b) Based on the boxplot in part (a), what percentage of Dr. Williams%u2019s students sent more than 64 texts in the previous day: less than 25%, between 25% and 50%, between 50% and 75%, or more than 75%? Do the data confirm Dr. Williams%u2019s suspicion? Explain your answer. 12. Copper mining Arizona%u2019s Copper World region yielded about 440,000 tons of high-quality copper from 1874 to 1969. Recently, a Canadian company found deposits of copper at shallow depths in this region. The company drilled test holes in several randomly selected locations at each of the old mine sites, and measured the amount of copper (as a percentage) in the rock extracted from each hole. Here are the data from the 28 test holes drilled at the Broad Top Butte site: 105 0.00 0.75 1.43 0.43 0.19 0.52 0.000.00 0.20 1.38 0.00 0.28 0.71 0.300.30 0.44 0.59 0.91 0.33 0.39 0.000.70 0.37 0.38 0.67 0.00 0.38 0.30pg 80pg 83 Exercises %u00a9 Bedford, Freeman & Worth Publishers. For review purposes only. Do not distribute.