At How Did I Do? How well did you do on the Chapter 1 Test? How well did you do relative to your classmates? Here are th

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At How Did I Do? How well did you do on the Chapter 1 Test? How well did you do relative to your classmates? Here are the results of a random sample of 20 of the Chapter 1 Tests, along with a dotplot and summary statistics Test Scores 61 65 65 73 75 77 78 78 79 80 80 80 80 81 811 88 89 93 98 99 60 65 70 75 80 85 Chapter 1 Test Scores n mean SD min Q1 med Q3 max 90 95 100 20 80 10 61 76 80 84.5 99 1. Biff scored a 65. What is Biff's percentile? 2. Was Biff above or below the mean? By how many points? By how many standard deviations? 3. Marty scored an 88. What is Marty's percentile? 4. Was Marty above or below the mean? By how many points? By how many standard deviations? A z-score is defined as the number of standard deviations above or below the mean. 5. Write a formula for calculating a z-score. 6. Goldie scored a 98 on the Chapter 1 Test. Find and interpret the Z-score. Bonus: Goldie was aspiring for what job? STATS MEDIC

7. There are two mathematical operations used when calculating a z-score: a. First, we take each score, and the mean (remember the mean was 80). Fill in the table and then make a dotplot for each. SCORE 61 65 65 73 75 77 78 78 79 80 80 80 80 81 81 88 89 93 98 99 SCORE- MEAN Dotplot for SCORE Dotplot for SCORE - MEAN 60 70 90 -10 20 HHH 80 100-20 10 What happens to the shape, center, and variability when you subtract the mean from each score? b. Second, we take the SCORE - MEAN and by the standard deviation (remember the standard deviation is 10). Fill in the table and then make a dotplot for each. SCORE - MEAN 19-15-15-7-5 -3 -2 -2 -1 0 0 0 0 1 1 8 9 13 18 19 SCORE- MEAN SD Dotplot for SCORE - MEAN SD HHH What happens to the shape, center, and variability when you divide by the standard deviation for each value? 8. Summarize: What happens to the shape, center and variability of a distribution when you ...add or subtract the same value a from each value? ...multiply or divide by the same value b from each value? 9. What is the mean and standard deviation of the distribution of Z-scores? Will this be true for any distribution of z-scores? Explain. + STATS MEDIC

Describing Location in a Distribution Important Ideas: Check Your Understanding: 1. According to an article on Yahoolnews, you should change your sheets every 7 days...at minimum. To investigate the sheet changing habits of adults, a random sample of 20 adults reported how often they change their sheets using an anonymous survey. Here is a dotplot and summary statistics of the results. %100 110 120 Time before changing sheets (dayo n mean SD min Q1 med 0, max 20 42.75 34.954 15 21 30 60 120 a. Suppose you convert the time before changing sheets from days to weeks. Describe the shape, mean, and standard deviation of the distribution of time before changing sheets in weeks. b. The adults in the study are given an article explaining the health benefits that would arise from changing their sheets more often. After reading the article each person agrees to change their sheets one week sooner than they used to. How does the shape.center, and variability of this distribution compare with the distribution of time in part (a)? c. Now suppose you convert the time before changing sheets from part (b) to z-scores. What would be the shape, mean, and standard deviation of this distribution? Explain your answers. + STATS MEDIC