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

rule Mean and Standard Deviation (numerical) Histogram (graphical) rule

3 The rule; applies only to mound-shaped data

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

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

6 Example: textbook costs

7 Example: textbook costs (cont.)

8 Example: textbook costs (cont.)

9 Example: textbook costs (cont.)

10 The best estimate of the standard deviation of the men’s weights displayed in this dotplot is

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

13 z-score corresponding to y

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?

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=( )/100=1.8 n Gerald’s z-score: z=(27-18)/6=1.5 n Eleanor’s score is better.

16 Z-scores add to zero Student/Institutional Support to Athletic Depts For the 9 Public ACC Schools: 2013 ($ millions) SchoolSupporty - ybarZ-score Maryland UVA Louisville UNC VaTech FSU GaTech NCSU Clemson Mean=9.1000, s= Sum = 0

17 In 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?

18 End of Section 2.4