Frequency Distributions Frequency Distribution Group Data into a

Frequency Distributions Frequency Distribution – Group Data into a set of k Ordered Classes Class Limits – Largest and Smallest Values in the Class Mark – Midpoint of the Class Frequency – Number of Observations within the Class

Example: Age Freq Guidelines: 18 -20 20 All Classes Should be: 21 -23 10 1) Of Equal Width 24 -26 5 2) Mutually Exclusive 27 -29 3 3) All-Inclusive 30&Up 2 40 Method: 24 = 16 1) Choose Number of Classes (Power of 2 Rule) n ≤ 2 k 25 = 32 26 = 64 2) Class Width > Range/k 3) Construct Frequency Distribution

Example: Injury Rate per Week per 1, 000 Work-Hrs 3. 0 2. 9 3. 2 3. 1 3. 6 3. 2 3. 8 2. 7 3. 2 3. 7 3. 3 4. 7 2. 6 2. 5 3. 7 2. 3 2. 8 3. 4 3. 1 2. 8 1. 8 3. 5 3. 4 3. 7 5. 3 4. 3 2. 4 3. 5 3. 3 3. 6 4. 2 3. 3 4. 6 4. 0 2. 6 3. 0 4. 3 3. 7 4. 0 2. 9 2. 1 3. 2 3. 9 3. 5 3. 9 4. 4 3. 1 4. 0

Injury Rate Freq 1. 8 – 2. 3 3 2. 4 – 2. 9 9 3. 0 – 3. 5 20 3. 6 – 4. 1 13 4. 2 – 4. 7 6 4. 8 – 5. 3 1 Rel Freq 52 Relative Frequency = Class Frequency/Number of Observations Example: St Petersburg Burbank Age Freq Rel Freq ~ ~ ~ 65&Up 90, 000 . 30 30, 000 . 15 300, 000 1. 00 200, 000 1. 00

Graphical Representations: Histogram – Bar Chart of a Frequency Distribution

Frequency Polygon – Line Chart of a Frequency Distribution

Cumulative Frequency – Number of Observations Up to a Point Injury Rate Cumulative Freq Less than 2. 4 Less than 3. 0 Less than 3. 6 Less than 4. 2 Less than 4. 8 Less than 5. 4 Injury Rate Freq Rel Freq 1. 8 – 2. 3 3 . 06 2. 4 – 2. 9 9 . 17 3. 0 – 3. 5 20 . 38 3. 6 – 4. 1 13 . 25 4. 2 – 4. 7 6 . 12 4. 8 – 5. 3 1 . 02 52 1. 00 Relative Cum Freq

Ogive Curve – A Graph of the Relative Cumulative Frequency

Stem & Leaf Analysis Age data: 17 18 Stem | Leaf 1 | 7899 2 | 0014 19 19 20 20 21 Break Stem into 2 Parts: Break Stem into 5 Parts Stem | Leaf 2* | 01234 2* | 01 2. | 56789 2 T | 23 2 digit Leaves: 2 F | 45 146 or 2 S | 67 2. | 89 1 | 4 1 | 5 24

Stem & Leaf Analysis of Injury Rate Data Cum Freq Stem | Leaf 1 1. | 8 4 2* | 134 12 2. | 56678899 (16) 3* | 0011122223333444 24 3. | 55556677778899 10 4* | 0002334 3 4. | 67 1 5* | 3

MPG achieved with 100 cars 19. 0 18. 2 21. 9 18. 8 20. 9 18. 9 22. 8 20. 2 17. 4 22. 4 20. 8 20. 5 20. 2 15. 1 18. 5 16. 6 22. 7 17. 3 19. 7 20. 4 22. 0 15. 3 14. 5 16. 5 20. 2 16. 8 21. 9 22. 6 19. 2 21. 6 22. 7 16. 2 14. 1 20. 5 18. 2 20. 8 22. 5 19. 3 16. 4 21. 3 10 Classes 20. 0 16. 3 22. 9 19. 1 20. 2 14. 7 17. 1 21. 7 21. 9 22. 4 15. 1 19. 1 21. 5 14. 3 20. 5 15. 4 22. 1 21. 6 21. 9 20. 3 21. 8 21. 6 22. 6 19. 2 18. 1 19. 3 17. 5 21. 7 23. 9 21. 1 19. 0 18. 7 19. 7 20. 7 15. 1 22. 9 20. 5 19. 2 18. 8 21. 5 18. 3 19. 2 17. 1 21. 3 20. 6 21. 7 22. 7 23. 9 21. 1 18. 6 22. 8 21. 4 16. 9 16. 8 18. 7 20. 4 19. 6 21. 9

5 Classes 20 Classes

Duration of Old Faithful

Mosaic Plot – Titanic Data