Frequency Distributions

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

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

3. Example: Injury Rate per Week per 1,000 Work-Hrs 3.0 2.9 3.2 3.1 3.6 3.2 3.8 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 3.4 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 3.3 3.7 4.0 2.9 2.1 3.2 3.9 3.5 3.5 3.9 4.4 3.1 4.0

4. Injury Rate Freq Rel 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 52 Relative Frequency = Class Frequency/Number of Observations Example: St Petersburg Burbank Age Freq Rel Freq Freq Rel Freq ~ ~ ~ ~ ~ 65&Up 90,000 .30 30,000 .15 300,000 1.00 200,000 1.00

5. Graphical Representations: Histogram – Bar Chart of a Frequency Distribution

6. Frequency Polygon – Line Chart of a Frequency Distribution

7. Cumulative Frequency – Number of Observations Up to a Point Injury Rate Cumulative Freq Relative Cum 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

8. Ogive Curve – A Graph of the Relative Cumulative Frequency

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

10. Stem & Leaf Analysis of Injury Rate Data Cum Freq Stem | Leaf 1 1. | 8 4 2* | 1 3 4 12 2. | 5 6 6 7 8 8 9 9 (16) 3* | 0 0 1 1 1 2 2 2 2 3 3 3 3 4 4 4 24 3. | 5 5 5 5 6 6 7 7 7 7 8 8 9 9 10 4* | 0 0 0 2 3 3 4 3 4. | 6 7 1 5* | 3

11. MPG achieved with 100 cars 19.0 20.8 22.0 22.7 20.0 15.1 21.8 21.1 21.5 21.1 18.2 20.5 15.3 16.2 16.3 19.1 21.6 19.0 18.3 18.6 21.9 20.2 14.5 14.1 22.9 21.5 22.6 18.7 19.2 22.8 18.8 15.1 16.5 20.5 19.1 14.3 19.2 19.7 17.1 21.4 20.9 18.5 20.2 18.2 20.2 20.5 18.1 20.7 21.3 16.9 18.9 16.6 16.8 20.8 14.7 15.4 19.3 15.1 20.6 16.8 22.8 22.7 21.9 22.5 17.1 22.1 17.5 22.9 21.7 18.7 20.2 17.3 22.6 19.3 21.7 21.6 21.7 20.5 22.7 20.4 17.4 19.7 19.2 16.4 21.9 21.9 21.7 19.2 23.9 19.6 22.4 20.4 21.6 21.3 22.4 20.3 23.9 18.8 21.1 21.9 10 Classes

12. 5 Classes 5 Classes 20 Classes

13. Duration of Old Faithful

14. Mosaic Plot – Titanic Data