2. 1 2.4 (cont.) Using the Mean and Standard Deviation Together 68-95-99.7 rule z-scores

3. 2 68-95-99.7 rule Mean and Standard Deviation (numerical) Histogram (graphical) 68-95-99.7 rule

4. 3 The 68-95-99.7 rule; applies only to mound-shaped data

5. 4 68-95-99.7 rule: 68% within 1 stan. dev. of the mean 68% 34% y-s y y+s

6. 5 68-95-99.7 rule: 95% within 2 stan. dev. of the mean 95% 47.5% y-2s y y+2s

7. 6 Example: textbook costs 286291307308315316327 328340342346347348348 349354355355360361364 367369371373377380381 382385385387390390397 398409409410418422424 425426428433434437440 480

8. 7 Example: textbook costs (cont.) 286291307308315316327328 340342346347348348349354 355355360361364367369371 373377380381382385385387 390390397398409409410418 422424425426428433434437 440480

9. 8 Example: textbook costs (cont.) 286291307308315316327328 340342346347348348349354 355355360361364367369371 373377380381382385385387 390390397398409409410418 422424425426428433434437 440480

10. 9 Example: textbook costs (cont.) 286291307308315316327328 340342346347348348349354 355355360361364367369371 373377380381382385385387 390390397398409409410418 422424425426428433434437 440480

11. 10 The best estimate of the standard deviation of the men’s weights displayed in this dotplot is 1. 10 2. 15 3. 20 4. 40

13. 12 Z-scores: Standardized Data Values Measures the distance of a number from the mean in units of the standard deviation

14. 13 z-score corresponding to y

15. 14 n Exam 1: y 1 = 88, s 1 = 6; exam 1 score: 91 Exam 2: y 2 = 88, s 2 = 10; exam 2 score: 92 Which score is better?

16. 15 Comparing SAT and ACT Scores n SAT Math: Eleanor’s score 680 SAT mean =500 sd=100 n ACT Math: Gerald’s score 27 ACT mean=18 sd=6 n Eleanor’s z-score: z=(680-500)/100=1.8 n Gerald’s z-score: z=(27-18)/6=1.5 n Eleanor’s score is better.

17. 16 Z-scores add to zero Student/Institutional Support to Athletic Depts For the 9 Public ACC Schools: 2013 ($ millions) SchoolSupporty - ybarZ-score Maryland15.56.41.79 UVA13.14.01.12 Louisville10.91.80.50 UNC9.20.10.03 VaTech7.9-1.2-0.34 FSU7.9-1.2-0.34 GaTech7.1-2.0-0.56 NCSU6.5-2.6-0.73 Clemson3.8-5.3-1.47 Mean=9.1000, s=3.5697 Sum = 0

18. 17 In 2007-08 the mean tuition at 4-yr public colleges/universities in the U.S. was $6185 with a standard deviation of $1804. In NC the mean tuition was $4320. What is NC’s z-score? 1. 1.03 2. -1.03 3. 2.39 4. 1865 5. -1865

19. 18 End of Section 2.4