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re of X = 84. Would you prel = = 10? (Hint: he location of

re of X = 84. Would you prel = = 10? (Hint: he location of

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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116 CHAPTER 4 MEASURES FOR VARIABILITY b. Now we break up the cluster in the center of the 7. On an exam with a mean of M = 78, you obtain a score of X= 84. a. Would you prefer a standard deviation of s = 2 or s = 10? (Hint: Sketch each distribution and find the location of your score.) distribution by moving two of the central scores out to the extremes. Once again compute the range and the standard deviation. New scores: 0 0 7 14 14 b. If your score were X = 72, would you prefer s = 2 or s = 10? Explain your answer. c. According to the range, how do the two distribu- tions compare in variability? How do they com- pare according to the standard deviation? 8. Calculate the mean and SS (sum of squared devia- tions) for each of the following samples. Based on the value for the mean, you should be able to decide which SS formula is better to use. 13. A population has a mean of µ = 30 and a standard deviation of o = 5. a. If 5 points were added to every score in the popu- lation, what would be the new values for the mean Sample A: 1 4 8. 5 Sample B: 3 0 9 4 and standard deviation? b. If every score in the population were multiplied by 3, what would be the new values for the mean 9. For the following population of N = 6 scores: 3 1 4 3 3 4 and standard deviation? a. Sketch a histogram showing the population distribution. 14. a. After 3 points have been added to every score in a sample, the mean is found to be M = 83 and b. Locate the value of the population mean in your the standard deviation is s = 8. What were the sketch, and make an estimate of the standard deviation (as done in Example 4.2). c. Compute SS, variance, and standard deviation for the population. (How well does your estimate compare with the actual value of o?) values for the mean and standard deviation for the original sample? b. After every score in a sample has been multiplied by 4, the mean is found to be M = 48 and the standard deviation is s = 12. What were the values for the mean and standard deviation for 10. For the following sample of n = 7 scores: the original sample? 8 6 5 2 6 3 5 15. For the following sample of n = 4 scores: 82, 88, 82, and 86: a. Sketch a histogram showing the sample distribution. b. Locate the value of the sample mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.5). c. Compute SS, variance, and standard deviation for the sample. (How well does your estimate with the actual value of s?) a. Simplify the arithmetic by first subtracting 80 points from each score to obtain a new sample of 2, 8, 2, and 6. Then, compute the mean and standard deviation for the new sample. b. Using the values you obtained in part a, what are compare the values for the mean and standard deviation for the original sample? 11. For the following population of N = 6 scores: 16. For the following sample of n = 8 scores: 0, 1, ;, 0, 3, ,0, and 1: a. Simplify the arithmetic by first multiplying each score by 2 to obtain a new sample of 0, 2, 1, 0, 6, 1, 0, and 2. Then, compute the mean and standard deviation for the new sample. b. Using the values you obtained in part a, what are 11 0 2 9 9 5 a. Calculate the range and the standard deviation. (Use either definition for the range.) b. Add 2 points to each score and compute the range and standard deviation again. Describe how adding a constant to each score influences measures of variability. the values for the mean and standard deviation for the original sample? 12. The range is completely determined by the two extreme scores in a distribution. The standard devia- tion, on the other hand, uses every score. 17. For the data in the following sample: 8 1 5 1 5 a. Compute the range (choose either definition) and the standard deviation for the following sample a. Find the mean and the standard deviation. of n = 5 scores. Note that there are three scores b. Now change the score of X = 8 to X = 18, and find the new mean and standard deviation. clustered around the mean in the center of the distribution, and two extreme values. c. Describe how one extreme score influences the Scores: 0 6 7 8 14 mean and standard deviation. Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Transcribed Image Text:116 CHAPTER 4 MEASURES FOR VARIABILITY b. Now we break up the cluster in the center of the 7. On an exam with a mean of M = 78, you obtain a score of X= 84. a. Would you prefer a standard deviation of s = 2 or s = 10? (Hint: Sketch each distribution and find the location of your score.) distribution by moving two of the central scores out to the extremes. Once again compute the range and the standard deviation. New scores: 0 0 7 14 14 b. If your score were X = 72, would you prefer s = 2 or s = 10? Explain your answer. c. According to the range, how do the two distribu- tions compare in variability? How do they com- pare according to the standard deviation? 8. Calculate the mean and SS (sum of squared devia- tions) for each of the following samples. Based on the value for the mean, you should be able to decide which SS formula is better to use. 13. A population has a mean of µ = 30 and a standard deviation of o = 5. a. If 5 points were added to every score in the popu- lation, what would be the new values for the mean Sample A: 1 4 8. 5 Sample B: 3 0 9 4 and standard deviation? b. If every score in the population were multiplied by 3, what would be the new values for the mean 9. For the following population of N = 6 scores: 3 1 4 3 3 4 and standard deviation? a. Sketch a histogram showing the population distribution. 14. a. After 3 points have been added to every score in a sample, the mean is found to be M = 83 and b. Locate the value of the population mean in your the standard deviation is s = 8. What were the sketch, and make an estimate of the standard deviation (as done in Example 4.2). c. Compute SS, variance, and standard deviation for the population. (How well does your estimate compare with the actual value of o?) values for the mean and standard deviation for the original sample? b. After every score in a sample has been multiplied by 4, the mean is found to be M = 48 and the standard deviation is s = 12. What were the values for the mean and standard deviation for 10. For the following sample of n = 7 scores: the original sample? 8 6 5 2 6 3 5 15. For the following sample of n = 4 scores: 82, 88, 82, and 86: a. Sketch a histogram showing the sample distribution. b. Locate the value of the sample mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.5). c. Compute SS, variance, and standard deviation for the sample. (How well does your estimate with the actual value of s?) a. Simplify the arithmetic by first subtracting 80 points from each score to obtain a new sample of 2, 8, 2, and 6. Then, compute the mean and standard deviation for the new sample. b. Using the values you obtained in part a, what are compare the values for the mean and standard deviation for the original sample? 11. For the following population of N = 6 scores: 16. For the following sample of n = 8 scores: 0, 1, ;, 0, 3, ,0, and 1: a. Simplify the arithmetic by first multiplying each score by 2 to obtain a new sample of 0, 2, 1, 0, 6, 1, 0, and 2. Then, compute the mean and standard deviation for the new sample. b. Using the values you obtained in part a, what are 11 0 2 9 9 5 a. Calculate the range and the standard deviation. (Use either definition for the range.) b. Add 2 points to each score and compute the range and standard deviation again. Describe how adding a constant to each score influences measures of variability. the values for the mean and standard deviation for the original sample? 12. The range is completely determined by the two extreme scores in a distribution. The standard devia- tion, on the other hand, uses every score. 17. For the data in the following sample: 8 1 5 1 5 a. Compute the range (choose either definition) and the standard deviation for the following sample a. Find the mean and the standard deviation. of n = 5 scores. Note that there are three scores b. Now change the score of X = 8 to X = 18, and find the new mean and standard deviation. clustered around the mean in the center of the distribution, and two extreme values. c. Describe how one extreme score influences the Scores: 0 6 7 8 14 mean and standard deviation. Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
PROBLEMS 85 PROBLEMS 10. A sample of n = 7 scores has a mean of M = 9. If one new person with a score of X = 1 is added to the sample, what is the value for the new mean? 1. Why is it necessary to have more than one method for measuring central tendency? 11. A sample of n = 6 scores has a mean of M = 13. If 2. Find the mean, median, and mode for the following sample of scores: one person with a score of X = 3 is removed from the sample, what is the value for the new mean? 12. A sample of n = 15 scores has a mean of M = 6. One person with a score of X = 22 is added to the sample. What is the value for the new sample mean? 4 5 2 7 1 3 3. Find the mean, median, and mode for the following sample of scores: 13. A sample of n = 10 scores has a mean of M = 9. One person with a score of X = 0 is removed from the sample. What is the value for the new sample mean? 3 6 7 3 9 8 3 7 5 4. Find the mean, median, and mode for the scores in 14. A population of N = 15 scores has a mean of u = 8. One score in the population is changed from X = 20 to X = 5. What is the value for the new population mean? the following frequency distribution table: f 15. A sample of n = 7 scores has a mean of M = 16. One score in the sample is changed from X = 6 to X = 20. What is the value for the new sample mean? 6 1 5 2 16. A sample of n = 7 scores has a mean of M = 5. After one new score is added to the sample, the new 4 3 2 2 2 mean is found to be M = 6. What is the value of the new score? (Hint: Compare the values for EX before and after the score was added.) 1 5 17. A population of N = 8 scores has a mean of p = 16. After one score is removed from the population, the new mean is found to be u = 15. What is the value of the score that was removed? (Hint: 5. Find the mean, median, and mode for the scores in the following frequency distribution table: f Compare the values for EX before and after the score was removed.) 8 1 7 1 18. A sample of n = 9 scores has a mean of M = 13. After one score is added to the sample, the mean is found to be M = 12. What is the value of the score 2 5 4 that was added? 2 19. A sample of n = 9 scores has a mean of M = 20. One of the scores is changed and the new mean is found to be M = 22. If the changed score was 6. For the following sample: originally X = 7, what is its new value? a. Assume that the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution. 20. One sample of n = 12 scores has a mean of M = 7 and a second sample of n = 8 scores has a mean of M = 12. If the two samples are combined, what is the mean for the combined sample? b. Assume that the scores are measurements of a discrete variable and find the median. 21. One sample has a mean of M = 8 and a second sample has a mean of M = 16. The two samples are combined into a single set of scores. Scores: 1 2 3 3 3 4 7. A population of N = 15 scores has EX = 120. What is the population mean? a. What is the mean for the combined set if both of the original samples have n = 4 scores? A sample ofn = 8 scores has a mean of M = 12. What is the value of EX for this sample? 8. b. What is the mean for the combined set if the first sample has n = 3 and the second sample 9. A population with a mean of µ = 8 has EX = 40. How many scores are in the population? has n = 5? Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Transcribed Image Text:PROBLEMS 85 PROBLEMS 10. A sample of n = 7 scores has a mean of M = 9. If one new person with a score of X = 1 is added to the sample, what is the value for the new mean? 1. Why is it necessary to have more than one method for measuring central tendency? 11. A sample of n = 6 scores has a mean of M = 13. If 2. Find the mean, median, and mode for the following sample of scores: one person with a score of X = 3 is removed from the sample, what is the value for the new mean? 12. A sample of n = 15 scores has a mean of M = 6. One person with a score of X = 22 is added to the sample. What is the value for the new sample mean? 4 5 2 7 1 3 3. Find the mean, median, and mode for the following sample of scores: 13. A sample of n = 10 scores has a mean of M = 9. One person with a score of X = 0 is removed from the sample. What is the value for the new sample mean? 3 6 7 3 9 8 3 7 5 4. Find the mean, median, and mode for the scores in 14. A population of N = 15 scores has a mean of u = 8. One score in the population is changed from X = 20 to X = 5. What is the value for the new population mean? the following frequency distribution table: f 15. A sample of n = 7 scores has a mean of M = 16. One score in the sample is changed from X = 6 to X = 20. What is the value for the new sample mean? 6 1 5 2 16. A sample of n = 7 scores has a mean of M = 5. After one new score is added to the sample, the new 4 3 2 2 2 mean is found to be M = 6. What is the value of the new score? (Hint: Compare the values for EX before and after the score was added.) 1 5 17. A population of N = 8 scores has a mean of p = 16. After one score is removed from the population, the new mean is found to be u = 15. What is the value of the score that was removed? (Hint: 5. Find the mean, median, and mode for the scores in the following frequency distribution table: f Compare the values for EX before and after the score was removed.) 8 1 7 1 18. A sample of n = 9 scores has a mean of M = 13. After one score is added to the sample, the mean is found to be M = 12. What is the value of the score 2 5 4 that was added? 2 19. A sample of n = 9 scores has a mean of M = 20. One of the scores is changed and the new mean is found to be M = 22. If the changed score was 6. For the following sample: originally X = 7, what is its new value? a. Assume that the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution. 20. One sample of n = 12 scores has a mean of M = 7 and a second sample of n = 8 scores has a mean of M = 12. If the two samples are combined, what is the mean for the combined sample? b. Assume that the scores are measurements of a discrete variable and find the median. 21. One sample has a mean of M = 8 and a second sample has a mean of M = 16. The two samples are combined into a single set of scores. Scores: 1 2 3 3 3 4 7. A population of N = 15 scores has EX = 120. What is the population mean? a. What is the mean for the combined set if both of the original samples have n = 4 scores? A sample ofn = 8 scores has a mean of M = 12. What is the value of EX for this sample? 8. b. What is the mean for the combined set if the first sample has n = 3 and the second sample 9. A population with a mean of µ = 8 has EX = 40. How many scores are in the population? has n = 5? Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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