1. Chapter 3 Modeling Distributions of Data Page 101

2. Lynette, who is a student in the class, is 65 inches tall. Is she tall or short relative to her classmates?

3. Measuring Location: PERCENTILES What percent of students in the class are Lynette’s height or shorter? 10/25=.4 Lynette is at the 40 th percentile in the class’s height distribution

4. Example 3.1 If Brett is 74 inches tall, what percentile does that put him in for the class’s height distribution? 23/25=0.92 or 92% 92 nd percentile

5. NOTE!! Some people define the pth percentile of a distribution as the value with p percent of observations BELOW it. Using this method, it is NEVER possible to be in the 100 th percentile Note the three people at 66 inches. Using the alternative method, they would be at the 40 th percentile (10/25=.4) instead of the 52 nd percentile (13/25=.52). Percentiles is not an exact science!!

6. Measuring Location: Z-Scores Where does Lynette’s height of 65 inches fall relative to the mean of this distribution? Since the mean height of the class is 67 inches, we can see that Lynette’s height is “below average.” But how much below average is it? By using Standard Deviation!

7. Measuring Location: Z-Scores The mean is 67 and the Standard Deviation is about 4 inches. We can say that Lynette’s height is about ½ standard deviation below the mean.

8. Measuring Location: Z-Scores

9. A z-score tells us how many standard deviations from the mean the original observation falls, and in what direction.

10. Example 3.2 Lynette’s height is about one-half of a standard deviation below the mean height of the class!!

11. Example 3.3 Sofia scores 660 on the SAT Math test. The distribution of SAT scores in the population is roughly symmetric and single-peaked with a mean 500 and standard deviation of 100. Jim takes the ACT Math test and scores 26. ACT scores follow a symmetric, single-peaked distribution with mean 18 and a standard deviation of 6. Assuming that both tests measure the same kind of ability, who did better?

12. SAT vs. ACT

13. Independent Practice Page 105-107 3.2-3.6 Evens (3 Questions) Hold onto homework until Friday!