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COURSE: JUST 3900 TIPS FOR APLIA Developed By: Ethan Cooper (Lead Tutor) John Lohman Michael Mattocks Aubrey Urwick Chapter 5: z-Scores

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Key Terms and Formulas: Don’t Forget Notecards

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Describing z-Scores Question 1: Identify the z-score value corresponding to each of the following locations in a distribution. Question 1: Identify the z-score value corresponding to each of the following locations in a distribution. Below the mean by 3 standard deviations. Below the mean by 3 standard deviations. Above the mean by 1/4 standard deviations. Above the mean by 1/4 standard deviations. Below the mean by 2.50 standard deviations. Below the mean by 2.50 standard deviations. Question 2: Describe the location in the distribution for each of the following z-scores. Question 2: Describe the location in the distribution for each of the following z-scores. z = - 1.50 z = - 1.50 z = 0.25 z = 0.25 z = - 3.50 z = - 3.50 z = 1.75 z = 1.75

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Describing z-Scores Question 1 Answer: Question 1 Answer: z = -3.00 z = -3.00 z = 0.25 z = 0.25 z = -2.50 z = -2.50 Question 2 Answer: Question 2 Answer: Below the mean by 1.50 standard deviations. Below the mean by 1.50 standard deviations. Above the mean by ¼ standard deviations. Above the mean by ¼ standard deviations. Below the mean by 3.50 standard deviations. Below the mean by 3.50 standard deviations. Above the mean by 1.75 standard deviations. Above the mean by 1.75 standard deviations.

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Describing z-Scores

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Transforming X-Values into z-Scores Question 3: For a distribution of µ = 40 and σ = 12, find the z-score for each of the following scores. Question 3: For a distribution of µ = 40 and σ = 12, find the z-score for each of the following scores. a) X = 36 b) X = 46 c) X = 56 Question 4: For a population with µ = 30 and σ = 8, find the z-score for each of the following scores. Question 4: For a population with µ = 30 and σ = 8, find the z-score for each of the following scores. a) X = 32 b) X = 26 c) X = 42

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Transforming X-Values into z-Scores

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Using z-Scores to Compare Different Populations Question 5: A distribution of English exam scores has µ = 70 and σ = 4. A distribution of history exam scores has µ = 60 and σ = 20. For which exam would a score of X = 78 have a higher standing? Explain your answer. Question 5: A distribution of English exam scores has µ = 70 and σ = 4. A distribution of history exam scores has µ = 60 and σ = 20. For which exam would a score of X = 78 have a higher standing? Explain your answer.

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Using z-Scores to Compare Different Populations Remember that 95% of all scores fall between ± 2.00. Thus, a score of +2.00 means that over 95% of the class scored below 78 on the English exam.

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Using z-Scores to Compare Different Populations Question 6: A distribution of English exam scores has µ = 50 and σ = 12. A distribution of history exam scores has µ = 58 and σ = 4. For which exam would a score of X = 62 have a higher standing? Explain your answer. Question 6: A distribution of English exam scores has µ = 50 and σ = 12. A distribution of history exam scores has µ = 58 and σ = 4. For which exam would a score of X = 62 have a higher standing? Explain your answer.

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Using z-Scores to Compare Different Populations

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z-Scores and Standardized Scores Question 7: A population of scores has µ = 73 and σ = 8. If the distribution is standardized to create a new distribution with µ = 100 and σ = 20, what are the new values for each of the following scores from the original distribution? Question 7: A population of scores has µ = 73 and σ = 8. If the distribution is standardized to create a new distribution with µ = 100 and σ = 20, what are the new values for each of the following scores from the original distribution? a) X = 65 b) X = 71 c) X = 81 d) X = 83

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z-Scores and Standardized Scores

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z-Scores and Standardized Scores Question 8: A population with a mean of µ = 44 and a standard deviation of σ = 6 is standardized to create a new distribution with µ = 50 and σ = 10. Question 8: A population with a mean of µ = 44 and a standard deviation of σ = 6 is standardized to create a new distribution with µ = 50 and σ = 10. a) What is the new standardized value for a score of X = 47 from the original distribution? b) One individual has a new standardized score of X = 65. What was this person’s score in the original distribution?

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z-Scores and Standardized Scores 44 505638 32 X = 47 z = 0.50 X = 55 Old Distribution z-Score Distribution New Standardized Distribution

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z-Scores and Standardized Scores 44 50 563832 X = 53 z = 1.50 X = 65 Old Distribution z-Score Distribution New Standardized Distribution

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Measure of Relative Location and Detecting Outliers Question 9: A sample has a mean of M = 30 and a standard deviation of s = 8. Question 9: A sample has a mean of M = 30 and a standard deviation of s = 8. a) Would a score of X = 36 be considered a central score or an extreme score in the sample? b) If the standard deviation were s = 2, would X = 36 be central or extreme?

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Measure of Relative Location and Detecting Outliers

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WARNING!!! The book defines an extreme score as being more than TWO standard deviations away from the mean. However, Aplia defines extreme scores as being more than THREE standard deviations from the mean. The book defines an extreme score as being more than TWO standard deviations away from the mean. However, Aplia defines extreme scores as being more than THREE standard deviations from the mean. When using Aplia, use the THREE definition of standard deviation for extreme scores. When using Aplia, use the THREE definition of standard deviation for extreme scores. On in class exercises and on the test, use the TWO definition of standard deviation for extreme scores. On in class exercises and on the test, use the TWO definition of standard deviation for extreme scores.

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Frequently Asked Questions FAQs XX - µ(X - µ) 2 1111 – 6 = 5(5) 2 = 25 00 – 6 = -6(-6) 2 = 36 22 – 6 = -4(-4) 2 = 16 29 – 6 = 3(3) 2 = 9 99 – 6 = 3(3) 2 = 9 55 – 6 = -1(-1) 2 = 1

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Frequently Asked Questions FAQs

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