Chapter 2: Frequency Distributions - My Websites

1 Chapter 2: Frequency Distributions Control Group Experimental Group 25 32 28 29. 27 20 25 31. 28 23 31 19. 17 21 29 35. 24 34 30 28. 22 29 24 30. 24 25 33 27. 21 18 34 26. 19 22 29 29. 30 24 27 32. 26 27 30 36. 24 23 22 23. 23 25 32 33. Control Group Experimental Group 16 18 20 22 24 26 28 30 32 34 16 18 20 22 24 26 28 30 32 34 36 Exam Score Exam Score 2 Example 8, 9, 8, 7, 10, 9, 6, 4, 9, 8, 7, 8, 10, 9, 8, 6, 9, 7, 8, 8, x f 10 2. 9 5. 8 7. 7 3. 6 2. 5 0. 4 1. 3 1 Example 8, 9, 8, 7, 10, 9, 6, 4, 9, 8, 7, 8, 10, 9, 8, 6, 9, 7, 8, 8, x f fx 10 2 20. 9 5 45. 8 7 56. 7 3 21. 6 2 12. 5 0 0. 4 1 4. 4 Example 8, 9, 8, 7, 10, 9, 6, 4, 9, 8, 7, 8, 10, 9, 8, 6, 9, 7, 8, 8, x f p=f/N %=p(100). 10 2 2/20= 10%. 9 5 5/20= 25%. 8 7 7/20= 35%.

2 7 3 3/20= 15%. 6 2 2/20= 10%. 5 0 0/20= 0%. 4 1 1/20= 5%. 5 Grouped Frequency distribution When a Frequency distribution table lists all of the individual categories (X values) it is called a regular Frequency distribution . Sometimes the scores covers a wide range of values: . 82, 75, 88, 93, 53, 84, 87, 58, 72, 94, 69, 84, 61, 91, 64, 87, 84, 70, 76, 89, 75, 80, 73, 73, 60 A list of all the X values is too long to be a simple . presentation of the data. To remedy this situation, a grouped Frequency distribution table is used. 2 Forming Class Intervals of a . Grouped Frequency distribution 1. Approximately 10 class intervals 2. Interval width a relatively simple number ( 2, 5, 10, or 20) 3. Bottom score of each interval a multiple of the width 4.

3 Same width 7 Table Grouped Frequency . distribution Table 82, 75, 88, 93, 53, 84, 87, 58, 72, 94, 69, 84, 61, 91, 64, 87, 84, 70, 76, 89, 75, 80, 73, 73, 60 x f 90-94 3. 85-89 4. 80-84 5. 75-79 4. 70-74 3. 65-69 1. 60-64 3. 55-59 1. 50-54 1 8 Frequency distribution Graphs 9 3 x f Frequency 6 1. 5 2. 4 4 2. 3 4. 2 2. 3 1 1. 2 1 1 2 3 4 5 6 7 Scores 10 Frequency x f 5 12-13. 4. 10-11. 5. 4 8-9. 3. 6-7. 3. 4-5. 2. 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Scores 11 20 15 Frequency 10 5 A B C Personality Type 12 4 x f Frequency 6 1. 5 2. 4 4 2. 3 4. 2 2. 3 1 1. 2 1 1 2 3 4 5 6 7 Scores 13 x f 6 1. Frequency 5 2. 4 2. 4 3 4. 2 2. 3 1 1. 2 1 1 2 3 4 5 6 7 Scores 14 Frequency x f 5 12-13. 4. 10-11. 5. 4 8-9. 3. 6-7. 3. 4-5. 2. 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Scores 15 5 Frequency x f 5 12-13.

4 4. 10-11. 5. 4 8-9. 3. 6-7. 3. 4-5. 2. 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Scores 16 30 25 x f 20 5 10 f 15 4 20 3 5 10 2 10 5 1 5 1 2 3 4 5 Score .60 .50 x f p .40 5 10 10/50= f .30 4 20 20/50= .20 3 5 5/50= .10 2 10 10/50= 1 5 5/50= 1 2 3 4 5 17 Score N=50 x f p % 5 10 10/50= 20% 4 20 20/50= 40% 3 5 5/50= 10% 2 10 10/50= 20% 1 5 5/50= 10% N=400 x f p % 5 80 80/400= 20% 4 160 160/400= 40% 3 40 40/400= 10% 2 80 80/400= 20% 1 40 40/400= 10% 18 6 19 Relative Frequency 68 84 100 116 132 IQ scores 20 Any distribution can be described by 3 characteristics: 1. Shape 2. Central tendency 3. Variability 21 7 Symmetrical Distributions Skewed Distributions Positive skew Negative skew 22 Frequency Distributions A B C D. E F G H.

5 23 Percentile Ranks and Percentiles : The percentage of scores in the distribution at or below a particular score is known as a percentile rank. The score corresponding to a specific percentile rank is known as a percentile score. 24 8 , , , , , , , , , , , , , , , , , 5 4 3 2 1 25 x f cf c% 5 1 20 100% 4 5 19 95% 3 8 14 70% 2 4 6 30% 1 2 2 10% 26 cf = 20 cf = 19 cf = 14 cf = 6 cf = 2 cf = 0 x = 1 x = 2 x = 3 x = 4 x = 5 f = 2 f = 4 f = 8 f = 5 f = 1 27 9 x f cf c% 100% 5 1 20 100% 95% 4 5 19 95% 70% 3 8 14 70% 30% 2 4 6 30% 10% 1 2 2 10% .5 0% 10% 28 6, 3, 7, 2, 8, 11, 6, 7, 16, 12, 9, 14, 8, 15, 9, 18, 7, 8, 21, 23 29 x f cf c% 20-24 2 20 100% 15-19 3 18 90% 10-14 3 15 75% 5-9 10 12 60% 0-4 2 2 10% 30 10 x f cf c% 100% 20-24 2 20 90% 15-19 3 18 75% 10-14 3 15 60% 5-9 10 12 10% 0-4 2 2 0 0% 31 Frequency 10 8 6 4 2 0-4 5-9 10-14 15-19 20-24 Scores 32 11