1. Descriptive Statistics Chapter 2

2. § 2.5 Measures of Position

3. Larson & Farber, Elementary Statistics: Picturing the World, 3e 3 Standard Scores The standard score or z - score, represents the number of standard deviations that a data value, x, falls from the mean, μ. Example : The test scores for all statistics finals at Union College have a mean of 78 and standard deviation of 7. Find the z - score for a.) a test score of 85, b.) a test score of 70, c.) a test score of 78. Continued.

4. Larson & Farber, Elementary Statistics: Picturing the World, 3e 4 Standard Scores Example continued : a.) μ = 78, σ = 7, x = 85 This score is 1 standard deviation higher than the mean. b.) μ = 78, σ = 7, x = 70 This score is 1.14 standard deviations lower than the mean. c.) μ = 78, σ = 7, x = 78 This score is the same as the mean.

5. Larson & Farber, Elementary Statistics: Picturing the World, 3e 5 Relative Z-Scores Example: John received a 75 on a test whose class mean was 73.2 with a standard deviation of 4.5. Samantha received a 68.6 on a test whose class mean was 65 with a standard deviation of 3.9. Which student had the better test score? John’s z - scoreSamantha’s z - score John’s score was 0.4 standard deviations higher than the mean, while Samantha’s score was 0.92 standard deviations higher than the mean. Samantha’s test score was better than John’s.

6. Larson & Farber, Elementary Statistics: Picturing the World, 3e 6 Exercises Pg 100-104 # 10, 21, 25-31, 35-38

7. Larson & Farber, Elementary Statistics: Picturing the World, 3e 7 Exercises # 10, 21, 25-31, 35-38 10 false, negative z-scores simply indicate that the data value is below the mean 21 2.8, 3.2, 3.65, 3.9, 4.6 25A z=-1.43, B z=0, C z=2.14 26 A z=-1.54, B z=0.77 C z=1.54 StatsBioBetter 27 1.43.77Stats 28 -.43-.77Stats 29 2.141.54Stats 30 00the same

8. Larson & Farber, Elementary Statistics: Picturing the World, 3e 8 Exercises # 10, 21, 25-31, 35-38 31 a -0.44, 0.89, -1.78 none seem particularly unusual b 2.5 th (no such thing) 84 th 50 th 35 1.66, -2.48, 3.72 the heights 62 and 80 inches are a bit unusual 36 0.28, -1.10, -0.07 none are particularly unusual 37.66 about the 70 th (from the graph) 38 -1 16 th (looks closer to 11 th on the graph)

9. Larson & Farber, Elementary Statistics: Picturing the World, 3e 9 Handout solutions 1a 30b 2 c 2d the same 2a 2.5b 1c -1d opposite 3a 5.71b -1.79c 0.26 4a 2.90b -2c 0 5 2.56 unusual 6 2.67 unusual 7 4.52 very unusual8 1.99 not unusual 9 -.42 -.38 -.38 psychology is better 10 A.47b.22c.6 best 37 Units of measure do not matter for z scores 38 60.475 inches

10. Larson & Farber, Elementary Statistics: Picturing the World, 3e 10 Handout solutions (continued)

11. Larson & Farber, Elementary Statistics: Picturing the World, 3e 11 Handout solutions (continued)

12. Larson & Farber, Elementary Statistics: Picturing the World, 3e 12 Handout solutions (continued)