Practice Problems (Describing Data Using Numerical Measures - Variability and z-scores) 1. Explain the concept of variability in plain English. 2. What does it mean for a sample to have a standard deviation of zero? Describe the scores in such a sample 3. What information is provided by the sign of the z-score? 4. What information is provided by the number for the z-score? Practice Problems (Describing Data Using Numerical Measures - Variability and z-scores) Page 1 5. Mechelle and Betty are both Administrative Assistants for Mark Frissora (the CEO of Caesars Entertainment Corporation). He has been receiving complaints about grammatical errors in emails being sent in his name (by his Administrative Assistants) and wants to find out who the likely culprit is. Mark begins keeping track of who sends emails under his name and collects data for a sample of 14 emails (7 from Mechelle and 7 from Betty) with the data below (use to answer a. - d.). Mechell e Betty 5 0 5 3 4 2 7 2 4 1 7 0 5 3 a. Calculate the mean for both Administrative Assistants. Which has a higher overall number of errors? X X Mechelle Betty = = Practice Problems (Describing Data Using Numerical Measures - Variability and z-scores) Page 2 Mechell e Betty 5 0 5 3 4 2 7 2 4 1 7 0 5 3 b. Calculate the standard deviation for both Administrative Assistants. Based on the standard deviation, is there much difference in how consistent each Administrative Assistants is? SMechelle = SBetty = c. Calculate the coefficient of variation for both Administrative Assistants. Based on the coefficient of variation, is there much difference in how consistent each Administrative Assistants is? CVMechelle = CVBetty = d. Explain why these two conclusions (from part b. and c.) differ. Practice Problems (Describing Data Using Numerical Measures - Variability and z-scores) Page 3 6. Eddie is the new General Manager at the Best Buy on Sunset Road in Henderson. Many Management positions recently opened up (after Eddie \"cleaned house\") and he wants to promote from within to fill these positions. In order to qualify for promotion consideration, employees must have an extremely high performance appraisal score from last quarter relative to the rest of the employees at Best Buy on Sunset Road. He is going to base this decision on z-scores. Specifically, employees with a z-score at or above 2 will qualify. Last quarter, the mean performance appraisal score was a 75 with a standard deviation of 5. Would the following employees qualify for the promotion (show z-score calculations to support your answer)? a. Quentin had a performance appraisal score of 85 last quarter. b. Amanda had a performance appraisal score of 82 last quarter. 7. You took a Math quiz ( = 35; = 4) with a score of 40/50, you took a Biology quiz ( = 70; = 2) with a score of 75/100, and you took a Psychology quiz ( = 80; = 10) with a score of 75/100. Which quiz did you perform better on relative to the rest of the class (2 points)? Show all of your work!! Practice Problems (Describing Data Using Numerical Measures - Variability and z-scores) Page 4 8. Fill in the z-score for each X when = 35; = 2.5 4 5 6 Frequency Look for a pattern that eliminates the need to perform calculations for all z-scores 25 27.5 30 32.5 35 37.5 40 42.5 45 47.5 1 z-scores: 22.5 2 3 Raw Quiz Scores (X) 20 Practice Problems (Describing Data Using Numerical Measures - Variability and z-scores) Page 5 50 Practice Problems (Describing Data Using Numerical Measures - Variability and z-scores) Page 6