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Identify the Outlier in the Data Set. Determine How the Outlier Affects the Mean, Median, and Mode of the Data

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Identify the Outlier in the Data Set. Determine How the Outlier Affects the Mean, Median, and Mode of the Data 11-5 Appropriate Measures 1. The number of minutes spent studying are: 60, 70, 45, 60, 80, 35, and 45. Find the measure of center that best represents the data. Justify your selection and then find the measure of center. ANSWER: The mean best represents the data. There are no extreme values. mean: 56.4 minutes median: 2. The table shows monthly rainfall in inches for five months. Identify the outlier in the data set. Determine how the outlier affects the mean, median, and mode of the data. Then tell which measure of center best describes the data with and without the outlier. Round to the nearest hundredth. Justify your selection. ANSWER: outlier: 2.43 in.; without the outlier: mean: 7.36 in., median: 7.19 in., mode: none; with the outlier: mean: 6.54 in., median: 6.83 in., mode: none; The mean rainfall best describes the data without the outlier. The median rainfall best describes the data with the outlier. 3. The table shows the average depth of several lakes. a. Identify the outlier in the data set. b. Determine how the outlier affects the mean, median, mode, and range eSolutionsof theManual data.- Powered by Cognero Page 1 c. Tell which measure of central tendency best describes the data with and without the outlier. ANSWER: a. 1,148 b. With the outlier, the mean is 216.83 ft, the median is 33.5 ft, there is no mode, and the range is 1,138. Without the outlier, the mean is 30.6 ft, the median is 24 ft, there is no mode, and the range is 52. c. With the outlier, the best measure is the median; without the outlier, the best measure is the mean. 4. Construct an Argument Fill in the graphic organizer below. ANSWER: 5. Find the Error Pilar is determining which measure of center best describes the data set{12, 18, 16, 44, 15, 15}. Find her mistake. ANSWER: Pilar did not include the outlier. The mean is 20. The median, which is 15.5, best describes the data because the outlier affects the mean more than it affects the median. 6. Justify Conclusions Determine whether the following statement is true or false. If true, explain your reasoning. If false, give a counterexample. Of mean, median, and mode, the median will always be most affected by outliers. ANSWER: false; Sample answer: Usually the mean is most affected by an outlier. In the data set 1, 4, 5, 6, and 24, the mean is 7.5 with the outlier and 4.2 without the outlier. 7. Persevere with Problems Add three data values to the following data set so the mean increases by 10 and the median does not change. 42, 37, 32, 29, 20 ANSWER: Sample answer: 125, 32, and 19 8. The table shows the greatest recorded weights of Florida’s fish. Which measure is most affected by the outlier? A. mean B. median C. mode D. range ANSWER: D 9. The number of songs downloaded per month by a group of friends were 8, 12, 6, 4, 2, 0, and 10. Find the measure of center that best represents the data. Justify your selection then find the measure of center. ANSWER: Since the set of data has no extreme values or numbers that are identical, the mean or median, 6 songs, would best represent the data. 10. The ages of participants in a relay race are 12, 15, 14, 13, 15, 12, 22, 16, and 11. Identify the outlier in the data set. Determine how the outlier affects the mean, median and mode of the data. Then tell which measure of center best describes the data with and without the outlier. ANSWER: outlier: 22 years; without the outlier: mean: 13.5 years, median: 13.5 years, mode: 12 years and 15 years; with the outlier: mean: 14.4 years, median: 14 years, mode: 12 years and 15 years; The modes best describes the data with and without the outlier, because it doesn't change. 11. Justify Conclusions The table shows the high temperatures during one week. Round to the nearest hundredth if necessary. a. Identify the outlier in the data set. b. Determine how the outlier affects the mean, median, mode, and range of the data. c. Tell which measure of center best describes the data with and without the outlier. Explain your reasoning to a classmate. ANSWER: o a. 62 b. With the outlier, the mean is 32.71o, the median is 29o and the range is o o o 37 . Without the outlier, the mean is 27.83 , the median is 28.5 , the mode is 29o, and the range is 4o. c. Sample answer: With the outlier, the best measure is the mode; without the outlier, the best measure is the mode; the outlier does not affect the mode, but affects the mean and median. 12. Find the measures of central tendency for the set of data. 17, 36, 45, 98, 25, 34, 19, 45, 36 A. mean: 41, median: 36, modes: 45 and 36, outlier: none B. mean: 41, median: 36, modes: 45 and 36, outliers: 98 and 19 C. mean: 39.4, median: 36, modes: 45 and 36, outlier: 98 D. mean: 39.4, median: 36, mode: 45, outlier: 98 ANSWER: C 13. Short Response Refer to Exercise 12. Which measure best describes the set of data? Explain. ANSWER: The median best describes the data with and without the outlier of 98 because it changes the least. With the outlier, the median is 36. Without the outlier, the median is 35, so it only decreased by 1. 14. The table shows the points a basketball team scored in different games. Which measure is most affected by the outlier? F. mean G. median H. mode I. range ANSWER: I 15. Short Response The times from a 100 meter race in seconds were: 12.5, 13.1, 11.9, 12.4, 12.7, 13.1, 12.6, and 12.2. What measure of center best represents the data? Explain. ANSWER: Sample answer: the mean and median times best represent the data. The mean is 12.56 s and the median is 12.55 s. There are no extreme values. Find the total of the set of numbers. 16. {19, 16, 24, 22, 18} ANSWER: 99 17. {54, 48, 52, 57, 49} ANSWER: 260 18. {9, 5, 6, 4, 11, 7} ANSWER: 49 19. {31, 36, 28, 34, 25} ANSWER: 154 20. Graph the numbers 15, 18, 22, 19, and 16 on the number line. ANSWER: 21. The table shows the number of tickets sold to the school musical on three days. How many total tickets were sold? ANSWER: 203 11-5 Appropriate Measures 1. The number of minutes spent studying are: 60, 70, 45, 60, 80, 35, and 45. Find the measure of center that best represents the data. Justify your selection and then find the measure of center. ANSWER: The mean best represents the data. There are no extreme values. mean: 56.4 minutes median: 2. The table shows monthly rainfall in inches for five months. Identify the outlier in the data set. Determine how the outlier affects the mean, median, and mode of the data. Then tell which measure of center best describes the data with and without the outlier. Round to the nearest hundredth. Justify your selection. ANSWER: outlier: 2.43 in.; without the outlier: mean: 7.36 in., median: 7.19 in., mode: none; with the outlier: mean: 6.54 in., median: 6.83 in., mode: none; The mean rainfall best describes the data without the outlier. The median rainfall best describes the data with the outlier. 3. The table shows the average depth of several lakes. a. Identify the outlier in the data set. b. Determine how the outlier affects the mean, median, mode, and range eSolutionsof theManual data.- Powered by Cognero Page 2 c. Tell which measure of central tendency best describes the data with and without the outlier. ANSWER: a. 1,148 b. With the outlier, the mean is 216.83 ft, the median is 33.5 ft, there is no mode, and the range is 1,138. Without the outlier, the mean is 30.6 ft, the median is 24 ft, there is no mode, and the range is 52. c. With the outlier, the best measure is the median; without the outlier, the best measure is the mean. 4. Construct an Argument Fill in the graphic organizer below. ANSWER: 5. Find the Error Pilar is determining which measure of center best describes the data set{12, 18, 16, 44, 15, 15}. Find her mistake. ANSWER: Pilar did not include the outlier. The mean is 20. The median, which is 15.5, best describes the data because the outlier affects the mean more than it affects the median. 6. Justify Conclusions Determine whether the following statement is true or false. If true, explain your reasoning. If false, give a counterexample. Of mean, median, and mode, the median will always be most affected by outliers. ANSWER: false; Sample answer: Usually the mean is most affected by an outlier. In the data set 1, 4, 5, 6, and 24, the mean is 7.5 with the outlier and 4.2 without the outlier. 7. Persevere with Problems Add three data values to the following data set so the mean increases by 10 and the median does not change. 42, 37, 32, 29, 20 ANSWER: Sample answer: 125, 32, and 19 8. The table shows the greatest recorded weights of Florida’s fish. Which measure is most affected by the outlier? A.
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