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

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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 11-5 Appropriate Measures mean rainfall best describes the data without the outlier. The median rainfall best describes the data with the outlier.

1. The number of minutes spent studying are: 60, 70, 45, 60, 80, 35, and 45. 3. The table shows the average depth of several lakes. 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 a. Identify the outlier in the data set. mean, median, and mode of the data. Then tell which measure of center b. Determine how the outlier affects the mean, median, mode, and range best describes the data with and without the outlier. Round to the of the data. nearest hundredth. Justify your selection. c. Tell which measure of central tendency best describes the data with ANSWER: and without the outlier. outlier: 2.43 in.; without the outlier: mean: 7.36 in., median: 7.19 in., mode: ANSWER: none; with the outlier: mean: 6.54 in., median: 6.83 in., mode: none; The a. 1,148 mean rainfall best describes the data without the outlier. The median rainfall best describes the data with the outlier. 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 3. The table shows the average depth of several lakes. 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: 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 5. Find the Error Pilar is determining which measure of center best b. With the outlier, the mean is 216.83 ft, the median is 33.5 ft, there is no describes the data set{12, 18, 16, 44, 15, 15}. mode, and the range is 1,138. Without the outlier, the mean is 30.6 ft, the Find her mistake. 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: 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. 5. Find the Error Pilar is determining which measure of center best Of mean, median, and mode, the median will always be most affected describes the data set{12, 18, 16, 44, 15, 15}. by outliers. Find her mistake. 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.

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. Which measure is most affected by the outlier? A. mean 7. Persevere with Problems Add three data values to the following data B. median set so the mean increases by 10 and the median does not change. C. mode 42, 37, 32, 29, 20 D. range ANSWER: ANSWER: Sample answer: 125, 32, and 19 D 8. The table shows the greatest recorded weights of Florida’s fish. 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 Which measure is most affected by the outlier? years, mode: 12 years and 15 years; with the outlier: mean: 14.4 years, A. mean median: 14 years, mode: 12 years and 15 years; The modes best B. median describes the data with and without the outlier, because it doesn't change. C. mode 11. Justify Conclusions The table shows the high temperatures during one D. range week. Round to the nearest hundredth if necessary. ANSWER: a. Identify the outlier in the data set. D b. Determine how the outlier affects the mean, median, mode, and range of the data. 9. The number of songs downloaded per month by a group of friends were c. Tell which measure of center best describes the data with and without 8, 12, 6, 4, 2, 0, and 10. Find the measure of center that best represents the outlier. Explain your reasoning to a classmate. the data. Justify your selection then find the measure of center. ANSWER: ANSWER: o a. 62 Since the set of data has no extreme values or numbers that are identical, o o the mean or median, 6 songs, would best represent the data. b. With the outlier, the mean is 32.71 , the median is 29 and the range is o o o 37 . Without the outlier, the mean is 27.83 , the median is 28.5 , the 10. The ages of participants in a relay race are 12, 15, 14, 13, 15, 12, 22, 16, o o mode is 29 , and the range is 4 . and 11. Identify the outlier in the data set. Determine how the outlier c. Sample answer: With the outlier, the best measure is the mode; without affects the mean, median and mode of the data. Then tell which measure the outlier, the best measure is the mode; the outlier does not affect the of center best describes the data with and without the outlier. mode, but affects the mean and median. ANSWER: outlier: 22 years; without the outlier: mean: 13.5 years, median: 13.5 12. Find the measures of central tendency for the set of data.

years, mode: 12 years and 15 years; with the outlier: mean: 14.4 years, 17, 36, 45, 98, 25, 34, 19, 45, 36 median: 14 years, mode: 12 years and 15 years; The modes best A. mean: 41, median: 36, modes: 45 and 36, outlier: none describes the data with and without the outlier, because it doesn't change. 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 11. Justify Conclusions The table shows the high temperatures during one D. mean: 39.4, median: 36, mode: 45, outlier: 98 week. Round to the nearest hundredth if necessary. a. Identify the outlier in the data set. ANSWER: b. Determine how the outlier affects the mean, median, mode, and range C of the data. c. Tell which measure of center best describes the data with and without 13. Short Response Refer to Exercise 12. Which measure best describes the outlier. Explain your reasoning to a classmate. the set of data? Explain. ANSWER: ANSWER: o The median best describes the data with and without the outlier of 98 a. 62 because it changes the least. With the outlier, the median is 36. Without o o b. With the outlier, the mean is 32.71 , the median is 29 and the range is the outlier, the median is 35, so it only decreased by 1. o o o 37 . Without the outlier, the mean is 27.83 , the median is 28.5 , the 14. The table shows the points a basketball team scored in different games. 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. Which measure is most affected by the outlier? 17, 36, 45, 98, 25, 34, 19, 45, 36 F. mean A. mean: 41, median: 36, modes: 45 and 36, outlier: none G. median B. mean: 41, median: 36, modes: 45 and 36, outliers: 98 and 19 H. mode C. mean: 39.4, median: 36, modes: 45 and 36, outlier: 98 I. range D. mean: 39.4, median: 36, mode: 45, outlier: 98 ANSWER: ANSWER: I C 15. Short Response The times from a 100 meter race in seconds were: 13. Short Response Refer to Exercise 12. Which measure best describes 12.5, 13.1, 11.9, 12.4, 12.7, 13.1, 12.6, and 12.2. What measure of center the set of data? Explain. best represents the data? Explain. ANSWER: ANSWER: The median best describes the data with and without the outlier of 98 Sample answer: the mean and median times best represent the data. The because it changes the least. With the outlier, the median is 36. Without mean is 12.56 s and the median is 12.55 s. There are no extreme values. the outlier, the median is 35, so it only decreased by 1. Find the total of the set of numbers. 14. The table shows the points a basketball team scored in different games. 16. {19, 16, 24, 22, 18} ANSWER: 99

17. {54, 48, 52, 57, 49} Which measure is most affected by the outlier? F. mean ANSWER: G. median 260 H. mode I. range 18. {9, 5, 6, 4, 11, 7} ANSWER: ANSWER: I 49 19. {31, 36, 28, 34, 25} 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 ANSWER: best represents the data? Explain. 154 ANSWER: 20. Graph the numbers 15, 18, 22, 19, and 16 on the number line. 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: ANSWER: 99

17. {54, 48, 52, 57, 49} 21. The table shows the number of tickets sold to the school musical on three days. How many total tickets were sold? ANSWER: 260

18. {9, 5, 6, 4, 11, 7} ANSWER: 49

19. {31, 36, 28, 34, 25} ANSWER: ANSWER: 154 203

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 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. 1. The number of minutes spent studying are: 60, 70, 45, 60, 80, 35, and 45. b. Determine how the outlier affects the mean, median, mode, and range Find the measure of center that best represents the data. Justify your of the data. selection and then find the measure of center. c. Tell which measure of central tendency best describes the data with ANSWER: and without the outlier. The mean best represents the data. There are no extreme values. mean: ANSWER: 56.4 minutes median: a. 1,148 2. The table shows monthly rainfall in inches for five months. 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. 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 4. Construct an Argument Fill in the graphic organizer below. 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. ANSWER: 3. The table shows the average depth of several lakes.

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.

4. Construct an Argument Fill in the graphic organizer below. 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. ANSWER: 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

5. Find the Error Pilar is determining which measure of center best 8. The table shows the greatest recorded weights of Florida’s fish. describes the data set{12, 18, 16, 44, 15, 15}. Find her mistake.

Which measure is most affected by the outlier? ANSWER: A. mean Pilar did not include the outlier. The mean is 20. The median, which is B. median 15.5, best describes the data because the outlier affects the mean more C. mode than it affects the median. D. range

6. Justify Conclusions Determine whether the following statement is true ANSWER: or false. If true, explain your reasoning. If false, give a counterexample. D eSolutions Manual - Powered by Cognero Page 2 Of mean, median, and mode, the median will always be most affected by outliers. 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 ANSWER: the data. Justify your selection then find the measure of center. false; Sample answer: Usually the mean is most affected by an outlier. In ANSWER: the data set 1, 4, 5, 6, and 24, the mean is 7.5 with the outlier and 4.2 without the outlier. 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. 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. 10. The ages of participants in a relay race are 12, 15, 14, 13, 15, 12, 22, 16, 42, 37, 32, 29, 20 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 ANSWER: of center best describes the data with and without the outlier. Sample answer: 125, 32, and 19 ANSWER: 8. The table shows the greatest recorded weights of Florida’s fish. 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 Which measure is most affected by the outlier? b. o o A. mean With the outlier, the mean is 32.71 , the median is 29 and the range is o o o B. median 37 . Without the outlier, the mean is 27.83 , the median is 28.5 , the C. mode mode is 29o, and the range is 4o. D. range 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 ANSWER: mode, but affects the mean and median. D 12. Find the measures of central tendency for the set of data. 9. The number of songs downloaded per month by a group of friends were 17, 36, 45, 98, 25, 34, 19, 45, 36 8, 12, 6, 4, 2, 0, and 10. Find the measure of center that best represents A. mean: 41, median: 36, modes: 45 and 36, outlier: none

the data. Justify your selection then find the measure of center. B. mean: 41, median: 36, modes: 45 and 36, outliers: 98 and 19 ANSWER: C. mean: 39.4, median: 36, modes: 45 and 36, outlier: 98 Since the set of data has no extreme values or numbers that are identical, D. mean: 39.4, median: 36, mode: 45, outlier: 98 the mean or median, 6 songs, would best represent the data. ANSWER: 10. The ages of participants in a relay race are 12, 15, 14, 13, 15, 12, 22, 16, C 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 13. Short Response Refer to Exercise 12. Which measure best describes of center best describes the data with and without the outlier. the set of data? Explain. ANSWER: ANSWER: outlier: 22 years; without the outlier: mean: 13.5 years, median: 13.5 The median best describes the data with and without the outlier of 98 years, mode: 12 years and 15 years; with the outlier: mean: 14.4 years, because it changes the least. With the outlier, the median is 36. Without median: 14 years, mode: 12 years and 15 years; The modes best the outlier, the median is 35, so it only decreased by 1. describes the data with and without the outlier, because it doesn't change. 14. The table shows the points a basketball team scored in different games. 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. Which measure is most affected by the outlier? c. Tell which measure of center best describes the data with and without F. mean the outlier. Explain your reasoning to a classmate. G. median ANSWER: H. mode o I. range a. 62 b. With the outlier, the mean is 32.71o, the median is 29o and the range is ANSWER: o o o I 37 . Without the outlier, the mean is 27.83 , the median is 28.5 , the o o mode is 29 , and the range is 4 . 15. Short Response The times from a 100 meter race in seconds were: c. Sample answer: With the outlier, the best measure is the mode; without 12.5, 13.1, 11.9, 12.4, 12.7, 13.1, 12.6, and 12.2. What measure of center the outlier, the best measure is the mode; the outlier does not affect the best represents the data? Explain. mode, but affects the mean and median. ANSWER: 12. Find the measures of central tendency for the set of data. Sample answer: the mean and median times best represent the data. The 17, 36, 45, 98, 25, 34, 19, 45, 36 mean is 12.56 s and the median is 12.55 s. There are no extreme values. A. mean: 41, median: 36, modes: 45 and 36, outlier: none B. mean: 41, median: 36, modes: 45 and 36, outliers: 98 and 19 Find the total of the set of numbers. 16. {19, 16, 24, 22, 18} C. mean: 39.4, median: 36, modes: 45 and 36, outlier: 98 D. mean: 39.4, median: 36, mode: 45, outlier: 98 ANSWER: 99 ANSWER: C 17. {54, 48, 52, 57, 49} Short Response 13. Refer to Exercise 12. Which measure best describes ANSWER: the set of data? Explain. 260 ANSWER: The median best describes the data with and without the outlier of 98 18. {9, 5, 6, 4, 11, 7} because it changes the least. With the outlier, the median is 36. Without ANSWER:

the outlier, the median is 35, so it only decreased by 1. 49

14. The table shows the points a basketball team scored in different games. 19. {31, 36, 28, 34, 25} ANSWER: 154

20. Graph the numbers 15, 18, 22, 19, and 16 on the number line. Which measure is most affected by the outlier? F. mean G. median

H. mode I. range ANSWER: ANSWER: I

15. Short Response The times from a 100 meter race in seconds were: 21. The table shows the number of tickets sold to the school musical on three 12.5, 13.1, 11.9, 12.4, 12.7, 13.1, 12.6, and 12.2. What measure of center days. How many total tickets were sold? 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: ANSWER: 99 203

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?

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.

The mean best represents the data. There are no extreme values. mean: a. Identify the outlier in the data set. 56.4 minutes median: b. Determine how the outlier affects the mean, median, mode, and range 2. The table shows monthly rainfall in inches for five months. of the data. c. Tell which measure of central tendency best describes the data with and without the outlier. ANSWER:

Identify the outlier in the data set. Determine how the outlier affects the a. 1,148 mean, median, and mode of the data. Then tell which measure of center b. With the outlier, the mean is 216.83 ft, the median is 33.5 ft, there is no best describes the data with and without the outlier. Round to the mode, and the range is 1,138. Without the outlier, the mean is 30.6 ft, the nearest hundredth. Justify your selection. 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 ANSWER: best measure is the mean. 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 4. Construct an Argument Fill in the graphic organizer below. 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.

ANSWER:

5. Find the Error Pilar is determining which measure of center best a. Identify the outlier in the data set. describes the data set{12, 18, 16, 44, 15, 15}. b. Determine how the outlier affects the mean, median, mode, and range Find her mistake. of the data. 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: 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. ANSWER: 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 5. Find the Error Pilar is determining which measure of center best set so the mean increases by 10 and the median does not change. describes the data set{12, 18, 16, 44, 15, 15}. 42, 37, 32, 29, 20 Find her mistake. ANSWER: Sample answer: 125, 32, and 19

8. The table shows the greatest recorded weights of Florida’s fish.

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 Which measure is most affected by the outlier? or false. If true, explain your reasoning. If false, give a counterexample. A. mean Of mean, median, and mode, the median will always be most affected B. median by outliers. C. mode D. range ANSWER: false; Sample answer: Usually the mean is most affected by an outlier. In ANSWER: the data set 1, 4, 5, 6, and 24, the mean is 7.5 with the outlier and 4.2 D without the outlier. 9. The number of songs downloaded per month by a group of friends were 7. Persevere with Problems Add three data values to the following data 8, 12, 6, 4, 2, 0, and 10. Find the measure of center that best represents set so the mean increases by 10 and the median does not change. the data. Justify your selection then find the measure of center. 42, 37, 32, 29, 20 ANSWER: 11-5ANSWER: Appropriate Measures Since the set of data has no extreme values or numbers that are identical, Sample answer: 125, 32, and 19 the mean or median, 6 songs, would best represent the data.

8. The table shows the greatest recorded weights of Florida’s fish. 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 Which measure is most affected by the outlier? of the data. A. mean c. Tell which measure of center best describes the data with and without B. median the outlier. Explain your reasoning to a classmate. C. mode ANSWER: D. range o a. 62 ANSWER: b. With the outlier, the mean is 32.71o, the median is 29o and the range is D o o o 37 . Without the outlier, the mean is 27.83 , the median is 28.5 , the 9. The number of songs downloaded per month by a group of friends were mode is 29o, and the range is 4o. 8, 12, 6, 4, 2, 0, and 10. Find the measure of center that best represents c. Sample answer: With the outlier, the best measure is the mode; without the data. Justify your selection then find the measure of center. the outlier, the best measure is the mode; the outlier does not affect the ANSWER: mode, but affects the mean and median. Since the set of data has no extreme values or numbers that are identical, 12. Find the measures of central tendency for the set of data. the mean or median, 6 songs, would best represent the data. 17, 36, 45, 98, 25, 34, 19, 45, 36 10. The ages of participants in a relay race are 12, 15, 14, 13, 15, 12, 22, 16, A. mean: 41, median: 36, modes: 45 and 36, outlier: none and 11. Identify the outlier in the data set. Determine how the outlier B. mean: 41, median: 36, modes: 45 and 36, outliers: 98 and 19 affects the mean, median and mode of the data. Then tell which measure C. mean: 39.4, median: 36, modes: 45 and 36, outlier: 98 of center best describes the data with and without the outlier. D. mean: 39.4, median: 36, mode: 45, outlier: 98 ANSWER: ANSWER: outlier: 22 years; without the outlier: mean: 13.5 years, median: 13.5 C years, mode: 12 years and 15 years; with the outlier: mean: 14.4 years, eSolutionsmedian: 14 years, mode: 12 Manual - Powered by Cogneroyears and 15 years; The modes best 13. Short Response Refer to Exercise 12. Which measure best describes Page 3 describes the data with and without the outlier, because it doesn't change. the set of data? Explain.

11. Justify Conclusions The table shows the high temperatures during one ANSWER: week. Round to the nearest hundredth if necessary. The median best describes the data with and without the outlier of 98 a. Identify the outlier in the data set. because it changes the least. With the outlier, the median is 36. Without b. Determine how the outlier affects the mean, median, mode, and range the outlier, the median is 35, so it only decreased by 1. of the data. 14. The table shows the points a basketball team scored in different games. 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 Which measure is most affected by the outlier? o o o F. mean 37 . Without the outlier, the mean is 27.83 , the median is 28.5 , the G. o o median mode is 29 , and the range is 4 . H. mode c. Sample answer: With the outlier, the best measure is the mode; without I. range the outlier, the best measure is the mode; the outlier does not affect the mode, but affects the mean and median. ANSWER: I 12. Find the measures of central tendency for the set of data. 17, 36, 45, 98, 25, 34, 19, 45, 36 15. Short Response The times from a 100 meter race in seconds were: A. mean: 41, median: 36, modes: 45 and 36, outlier: none 12.5, 13.1, 11.9, 12.4, 12.7, 13.1, 12.6, and 12.2. What measure of center B. mean: 41, median: 36, modes: 45 and 36, outliers: 98 and 19 best represents the data? Explain. C. mean: 39.4, median: 36, modes: 45 and 36, outlier: 98 ANSWER: D. mean: 39.4, median: 36, mode: 45, outlier: 98 Sample answer: the mean and median times best represent the data. The ANSWER: mean is 12.56 s and the median is 12.55 s. There are no extreme values. C Find the total of the set of numbers. 13. Short Response Refer to Exercise 12. Which measure best describes 16. {19, 16, 24, 22, 18} the set of data? Explain. ANSWER: ANSWER: 99 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 17. {54, 48, 52, 57, 49} the outlier, the median is 35, so it only decreased by 1. ANSWER: 14. The table shows the points a basketball team scored in different games. 260 18. {9, 5, 6, 4, 11, 7} ANSWER: 49

Which measure is most affected by the outlier? 19. {31, 36, 28, 34, 25} F. mean G. median ANSWER: H. mode 154 I. range 20. Graph the numbers 15, 18, 22, 19, and 16 on the number line. 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 ANSWER: 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. 21. The table shows the number of tickets sold to the school musical on three days. How many total tickets were sold? Find the total of the set of numbers. 16. {19, 16, 24, 22, 18} ANSWER: 99

17. {54, 48, 52, 57, 49} ANSWER: 260 ANSWER: 203 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?

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.

1. The number of minutes spent studying are: 60, 70, 45, 60, 80, 35, and 45. a. Identify the outlier in the data set. Find the measure of center that best represents the data. Justify your b. Determine how the outlier affects the mean, median, mode, and range selection and then find the measure of center. of the data. ANSWER: c. Tell which measure of central tendency best describes the data with The mean best represents the data. There are no extreme values. mean: and without the outlier. 56.4 minutes median: ANSWER: 2. The table shows monthly rainfall in inches for five months. 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 Identify the outlier in the data set. Determine how the outlier affects the best measure is the mean. 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 4. Construct an Argument Fill in the graphic organizer below. 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. ANSWER: 3. The table shows the average depth of several lakes.

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.

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 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. ANSWER: c. With the outlier, the best measure is the median; without the outlier, the Pilar did not include the outlier. The mean is 20. The median, which is best measure is the mean. 15.5, best describes the data because the outlier affects the mean more than it affects the median. 4. Construct an Argument Fill in the graphic organizer below. 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 ANSWER: 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 5. Find the Error Pilar is determining which measure of center best describes the data set{12, 18, 16, 44, 15, 15}. 8. The table shows the greatest recorded weights of Florida’s fish. Find her mistake.

ANSWER: Which measure is most affected by the outlier? Pilar did not include the outlier. The mean is 20. The median, which is A. mean 15.5, best describes the data because the outlier affects the mean more B. median than it affects the median. C. mode D. range 6. Justify Conclusions Determine whether the following statement is true or false. If true, explain your reasoning. If false, give a counterexample. ANSWER: Of mean, median, and mode, the median will always be most affected D by outliers. 9. The number of songs downloaded per month by a group of friends were ANSWER: 8, 12, 6, 4, 2, 0, and 10. Find the measure of center that best represents false; Sample answer: Usually the mean is most affected by an outlier. In the data. Justify your selection then find the measure of center. the data set 1, 4, 5, 6, and 24, the mean is 7.5 with the outlier and 4.2 ANSWER: without the outlier. Since the set of data has no extreme values or numbers that are identical, 7. Persevere with Problems Add three data values to the following data the mean or median, 6 songs, would best represent the data. set so the mean increases by 10 and the median does not change. 42, 37, 32, 29, 20 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 ANSWER: affects the mean, median and mode of the data. Then tell which measure Sample answer: 125, 32, and 19 of center best describes the data with and without the outlier.

8. The table shows the greatest recorded weights of Florida’s fish. 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 Which measure is most affected by the outlier? a. 62 A. mean b. With the outlier, the mean is 32.71o, the median is 29o and the range is B. median o o o C. mode 37 . Without the outlier, the mean is 27.83 , the median is 28.5 , the o o D. range mode is 29 , and the range is 4 . c. Sample answer: With the outlier, the best measure is the mode; without ANSWER: the outlier, the best measure is the mode; the outlier does not affect the D mode, but affects the mean and median.

9. The number of songs downloaded per month by a group of friends were 12. Find the measures of central tendency for the set of data. 8, 12, 6, 4, 2, 0, and 10. Find the measure of center that best represents 17, 36, 45, 98, 25, 34, 19, 45, 36 the data. Justify your selection then find the measure of center. A. mean: 41, median: 36, modes: 45 and 36, outlier: none ANSWER: B. mean: 41, median: 36, modes: 45 and 36, outliers: 98 and 19 Since the set of data has no extreme values or numbers that are identical, C. mean: 39.4, median: 36, modes: 45 and 36, outlier: 98 the mean or median, 6 songs, would best represent the data. D. mean: 39.4, median: 36, mode: 45, outlier: 98

10. The ages of participants in a relay race are 12, 15, 14, 13, 15, 12, 22, 16, ANSWER: and 11. Identify the outlier in the data set. Determine how the outlier C affects the mean, median and mode of the data. Then tell which measure of center best describes the data with and without the outlier. 13. Short Response Refer to Exercise 12. Which measure best describes the set of data? Explain. ANSWER: outlier: 22 years; without the outlier: mean: 13.5 years, median: 13.5 ANSWER: years, mode: 12 years and 15 years; with the outlier: mean: 14.4 years, The median best describes the data with and without the outlier of 98 median: 14 years, mode: 12 years and 15 years; The modes best because it changes the least. With the outlier, the median is 36. Without describes the data with and without the outlier, because it doesn't change. the outlier, the median is 35, so it only decreased by 1.

11. Justify Conclusions The table shows the high temperatures during one 14. The table shows the points a basketball team scored in different games. 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 Which measure is most affected by the outlier? the outlier. Explain your reasoning to a classmate. F. mean ANSWER: G. median H. mode a. o 62 I. range b. With the outlier, the mean is 32.71o, the median is 29o and the range is o o o ANSWER: 37 . Without the outlier, the mean is 27.83 , the median is 28.5 , the I mode is 29o, and the range is 4o. c. Sample answer: With the outlier, the best measure is the mode; without 15. Short Response The times from a 100 meter race in seconds were: the outlier, the best measure is the mode; the outlier does not affect the 12.5, 13.1, 11.9, 12.4, 12.7, 13.1, 12.6, and 12.2. What measure of center mode, but affects the mean and median. best represents the data? Explain. 12. Find the measures of central tendency for the set of data. ANSWER: 17, 36, 45, 98, 25, 34, 19, 45, 36 Sample answer: the mean and median times best represent the data. The A. mean: 41, median: 36, modes: 45 and 36, outlier: none mean is 12.56 s and the median is 12.55 s. There are no extreme values. B. mean: 41, median: 36, modes: 45 and 36, outliers: 98 and 19 Find the total of the set of numbers. C. mean: 39.4, median: 36, modes: 45 and 36, outlier: 98 16. {19, 16, 24, 22, 18} D. mean: 39.4, median: 36, mode: 45, outlier: 98 ANSWER: ANSWER: 11-5 Appropriate Measures 99 C

13. Short Response Refer to Exercise 12. Which measure best describes 17. {54, 48, 52, 57, 49}

the set of data? Explain. ANSWER: ANSWER: 260 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 18. {9, 5, 6, 4, 11, 7} the outlier, the median is 35, so it only decreased by 1. ANSWER: 14. The table shows the points a basketball team scored in different games. 49 19. {31, 36, 28, 34, 25} ANSWER: 154

Which measure is most affected by the outlier? 20. Graph the numbers 15, 18, 22, 19, and 16 on the number line. F. mean G. median H. mode

I. range ANSWER: 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 21. The table shows the number of tickets sold to the school musical on three best represents the data? Explain. days. How many total tickets were sold? 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 ANSWER: 203 17. {54, 48, 52, 57, 49} ANSWER: eSolutions260 Manual - Powered by Cognero Page 4

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