1. AP Statistics Wednesday, 23 September 2015 OBJECTIVE TSW (1) quiz over means, boxplots, and variability, and (2) review for Friday’s test. GET OUT –WS Interpreting Center and Variability After QUIZ: Means, Boxplots & Variability, work on WS AP Review: Center, Spread, Boxplots. TEST: Measuring and Interpreting Variability –Friday, 25 September 2015

2. WS Interpreting Center and Variability 1)a)81.5% b)2.5% c)16 th percentile 2)Ralph had the better score. (Ralph’s z-score = 1.4285… Louise’s z-score = 1.1428…) 3)a)50% b)16% c)95% d)70 inches

3. WS Interpreting Center and Variability 4)a)0.16 b)0.84 c)About 136 cups (based on 8-ounce cups) 5)At least 19% z-score = 1.1111… The distribution is (negatively) skewed, so use Chebyshev’s Rule: k = 1.1111… 100(1 – 1 /( 1.1111... ) 2 )% = 18.9999…%

4. Examples Ms. Havens’ 9 th period Stat class had quiz scores of 76, 84, 95, 100, 63, 87, and 90. Billy Bob was absent and took the quiz later, scoring a 70. What was his z-score? Calculate without Billy Bob’s score. Mean (  ) = 85 Standard deviation (  ) = 11.464 z-score = 70 – 85 / 11.464 = –1.308

5. Examples A 10% trimmed mean takes off 10% of the smallest data items and 10% of the largest data items from a list. In a list of 200 items, how many items would be used to calculate the mean? 160 items

6. Examples For Chebyshev’s Rule, what percent of observations are within 2.3 SD of the mean? 100 ( 1 – 1 /2.3 2 )% 81.096%

7. Examples In a right-skewed distribution, which is larger, the mean or the median? the mean

8. Examples In a normal distribution, what percent of observations are between 3 SD below and 1 SD above the mean? 83.85%

9. Examples Which measure of variability is resistant? IQR

10. TEST TOPICS Data Analysis

11. TEST TOPICS Data Analysis 4 Calculate mean and median. –Calculate weighted mean. –Calculate trimmed mean. 4 Calculate variance and standard deviation. –Population vs. Sample. 4 Given a data set, define the quartiles. 4 Interpret a box plot. 4 Know the resistant measures to outliers. 4 Apply Chebyshev’s Rule.

12. TEST TOPICS Data Analysis 4 Calculate z-scores. 4 Know the characteristics of z-scores. 4 Know the Empirical Rule. 4 Calculate percentiles using Chebyshev’s Rule and z-scores. 4 Use the Linear Transformation Rule. 4 Wear a (preferably purple) JVHS shirt to receive a dropped daily grade.

13. QUIZ: Means, Boxplots & Variability When you finish the quiz, bring it to me and pick up WS AP Review: Center, Spread, Boxplots. – We will go over this after lunch. TEST TOPICS will be given after lunch.

14. QUIZ: Means, Boxplots, & Variability ANSWERS 1)squared deviations 2)symmetrical 3)true 4)increased by a factor of 3 5)less than 6)sometimes

15. 7)Coca-Cola was most volatile since its range was the largest. 8)McDonald’s had more weekly declines. Its median was the only median that was negative, so at least half of McDonald’s weekly percentage changes were declines. 9)Shape The distribution is fairly symmetrical. Center The center (median) is 24.5 months. Spread And the spread (range) is 69 months. 10 20 30 40 50 60 70 # months at current position QUIZ: Means, Boxplots, & Variability ANSWERS

16. 10)z = 6 – 3.75 / 3.767 = 0.597 11)13.5 + 34 + 34 = 81.5% 12)100(1 – 1 / 1.4 2 ) = 48.980% QUIZ: Means, Boxplots, & Variability ANSWERS

17. WS AP Review – Center, Spread, Boxplots ANSWERS 1)C 2)E 3)B 4)A 5)C 6)B 7)E 8)C 9)A 10)B 11)C 12)A