1. Welcome to MM150 Seminar 9: Statistics, Part II To resize your pods: Place your mouse here. Left mouse click and hold. Drag to the right to enlarge the pod. To maximize chat, minimize roster by clicking here

2. Measures of Central Tendency

3. Measures of Central Tendency section 9.1 The mean of a set of numbers is the average. Example:12, 5, 7, 16 mean = (12+5+7+16)/4 = 10

4. Measures of Central Tendency section 9.1 Example:The mean of five test scores is 81. What is the sum of the test scores?

5. Measures of Central Tendency section 9.1 page 368 #37

6. Measures of Central Tendency section 9.1 The median of a set of numbers is the middle number. Example:5, 3, 11, 9, 8, 15, 2 Order the numbers: 2,3,5,8,9,11,15 The median is the middle number = 8

7. Measures of Central Tendency section 9.1 If there are an even number of values: Example:5, 3, 11, 9, 8, 15, 2, 20 Order the numbers: 2,3,5,8,9,11,15, 20 The median is the average of the middle numbers = (8+9)/2 = 8.5

8. Measures of Central Tendency section 9.1 Mode = most frequently occurring value (may have more than one mode) ex: 1,1,2,2,2,5,7,8,8,8,9 Midrange = (low val + high val) / 2

9. Measures of Central Tendency section 9.1 Values: 2 3 7 9 10 13 17 21 22 25 30 Median = "50th percentile" = Q2 First Quartile = median of lower half = Q1 Third Quartile = median of upper half = Q3

10. Measures of Central Tendency section 9.1 Values: 15191920222324 24242526272930 32343435363942 What are Q 1, Q 2 and Q 3 ?

11. Measures of Central Tendency section 9.1 Page 368 #51

12. Measures of Dispersion

13. Measures of Dispersion section 9.2 Two data sets with mean = 50 Data Set 1:48, 49, 50, 51, 52 Data Set 2:10, 20, 50, 80, 90 What is the difference?

14. Measures of Dispersion section 9.2 Range = high val - low val Example:11, 9, 6, 12, 17 What is the range?

15. Measures of Dispersion section 9.2 Standard Deviation: "average" deviation from the mean Data Set:2, 3, 5, 8, 9, 11, 18

16. The Normal Curve

17. The Normal Curve section 9.3 Data which approximates a Normal Distribution

18. The Normal Curve section 9.3

19. Use table 9.4 to find the area to the right of z = 1.34

20. The Normal Curve section 9.3 Use table 9.4 to find the area to the left of z = 1.62

21. The Normal Curve section 9.3 Use table 9.4 to find the area between z = -1.32 and z = -1.64

22. The Normal Curve section 9.3 Page 394 #49

23. The Normal Curve section 9.3 Page 394 #50

24. The Normal Curve section 9.3 Assume that math SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. What percent of students who took the test have a math score below 550?

25. The Normal Curve section 9.3 Assume that math SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. What percent of students who took the test have a math score above 650?

26. The Normal Curve section 9.3 Assume that math SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. What percent of students who took the test have a math score between 550 and 650?

27. Linear Regression