1. 1 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY S TATISTICS Section 2-6 Measures of Position

2. 2 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Measures of Position

3. 3 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman  z Score (or standard score) the number of standard deviations that a given value x is above or below the mean Measures of Position

4. 4 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Sample z = x - x s Measures of Position z score

5. 5 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Sample z = x - x s Population z = x - µ  Measures of Position z score

6. 6 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Sample z = x - x s Population z = x - µ  Round to 2 decimal places Measures of Position z score

7. 7 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman - 3- 2- 101 23 Z Unusual Values Unusual Values Ordinary Values Interpreting Z Scores FIGURE 2-16

8. 8 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Measures of Position Quartiles, Deciles, Percentiles

9. 9 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Quartiles

10. 10 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Q 1, Q 2, Q 3 Quartiles

11. 11 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Q 1, Q 2, Q 3 divides ranked scores into four equal parts Quartiles

12. 12 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Q 1, Q 2, Q 3 divides ranked scores into four equal parts Quartiles 25% Q3Q3 Q2Q2 Q1Q1

13. 13 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Q 1, Q 2, Q 3 divides ranked scores into four equal parts Quartiles 25% Q3Q3 Q2Q2 Q1Q1 (minimum)(maximum) (median)

14. 14 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman D 1, D 2, D 3, D 4, D 5, D 6, D 7, D 8, D 9 divides ranked data into ten equal parts Deciles

15. 15 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman D 1, D 2, D 3, D 4, D 5, D 6, D 7, D 8, D 9 divides ranked data into ten equal parts Deciles 10% D 1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9

16. 16 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 99 Percentiles Percentiles

17. 17 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Quartiles, Deciles, Percentiles Fractiles

18. 18 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Quartiles, Deciles, Percentiles Fractiles (Quantiles) partitions data into approximately equal parts

19. 19 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Finding the Percentile of a Given Score

20. 20 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Finding the Percentile of a Given Score Percentile of score x = 100 number of scores less than x total number of scores

21. 21 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Finding the Score Given a Percentile

22. 22 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Finding the Score Given a Percentile n total number of values in the data set k percentile being used L locator that gives the position of a value P k k th percentile L = n k 100

23. 23 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Finding the Value of the kth Percentile Sort the data. (Arrange the data in order of lowest to highest.) The value of the kth percentile is midway between the Lth value and the next value in the sorted set of data. Find P k by adding the L th value and the next value and dividing the total by 2. Start Compute L = n where n = number of values k = percentile in question ) ( k 100 Change L by rounding it up to the next larger whole number. The value of P k is the Lth value, counting from the lowest Is L a whole number ? Yes No Figure 2-17

24. 24 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Quartiles Q 1 = P 25 Q 2 = P 50 Q 3 = P 75

25. 25 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Quartiles Q 1 = P 25 Q 2 = P 50 Q 3 = P 75 D 1 = P 10 D 2 = P 20 D 3 = P 30 D 9 = P 90 Deciles

26. 26 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Interquartile Range (or IQR): Q 3 - Q 1

27. 27 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Interquartile Range (or IQR): Q 3 - Q 1 Semi-interquartile Range: 2 Q 3 - Q 1

28. 28 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Interquartile Range (or IQR): Q 3 - Q 1 Semi-interquartile Range: Midquartile: 2 2 Q 3 - Q 1 Q 1 + Q 3

29. 29 Chapter 2. Section 2-6. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Interquartile Range (or IQR): Q 3 - Q 1 Semi-interquartile Range: Midquartile: 10 - 90 Percentile Range: P 90 - P 10 2 2 Q 3 - Q 1 Q 1 + Q 3