1. Chapter 2: Frequency Distributions

2. 2 Control GroupExperimental Group 16182022242628303234 Control Group Exam Score 16182022242628303234 Experimental Group Exam Score 36 Control vs. Experimental Example

3. 3 Example 2.1 8, 9, 8, 7, 10, 9, 6, 4, 9, 8, 7, 8, 10, 9, 8, 6, 9, 7, 8, 8,

4. 4 Example 2.1b 8, 9, 8, 7, 10, 9, 6, 4, 9, 8, 7, 8, 10, 9, 8, 6, 9, 7, 8, 8,

5. 5 Example 2.2 8, 9, 8, 7, 10, 9, 6, 4, 9, 8, 7, 8, 10, 9, 8, 6, 9, 7, 8, 8,

6. 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.

7. 7 Forming Class Intervals of a Grouped Frequency Distribution 1.Approximately 10 class intervals 2.Interval width a relatively simple number (e.g. 2, 5, 10, or 20) 3.Bottom score of each interval a multiple of the width 4.Same width

8. 8 Table 2.2 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

9. Frequency Distribution Graphs 9

10. 10 Scores 4 3 2 1 1234567 Frequency Simple Frequency distribution

11. 11 4 3 2 1 1234567 Scores Frequency 891011121314 5 Grouped frequency Distribution

12. 12 5 10 15 20 Frequency Personality Type ABC Frequency vs. Personality type

13. 13 Scores 4 3 2 1 1234567 Frequency Simple Frequency distribution

14. 14 4 3 2 1 1234567 Scores Frequency Frequency bar graph

15. 15 4 3 2 1 1234567 Scores Frequency 891011121314 5 Grouped frequency Distribution

16. 16 4 3 2 1 1234567 Scores Frequency 891011121314 5 Grouped frequency bar graph

17. 17 5 10 15 20 25 30 12345 Score f.10.20.30.40.50.60 12345 Score f xf 510 420 35 210 15 Frequency vs. Percentages graphs xfp 51010/50=0.20 42020/50=0.40 355/50=0.10 21010/50=0.20 155/50=0.10

18. 18 xfp% 51010/50=0.2020% 42020/50=0.4040% 355/50=0.1010% 21010/50=0.2020% 155/50=0.1010% xfp% 58080/400=0.2020% 4160160/400=0.4040% 34040/400=0.1010% 28080/400=0.2020% 14040/400=0.1010% N=50 N=400 Data tables showing percentages

19. 19 Normal distribution of scores

20. 20 1001321166884 IQ scores Relative frequency IQ score distribution

21. 21 Any distribution can be described by 3 characteristics: 1.Shape 2.Central tendency 3.Variability

22. 22 Symmetrical Distributions Skewed Distributions Positive skew Negative skew Symmetrical vs. Non- symmetrical examples

23. 23 ABCD HGF E Frequency Distributions

24. 24 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.

25. 25 1.3, 5.2, 4.0, 4.2, 3.0, 2.1, 4.3, 2.9, 1.0 3.8, 3.9, 3.3, 3.1, 1.9, 3.4, 2.2, 2.9, 1.8 3.0, 2.7 5432154321 Numbers grouped by color

26. 26 xfcfc% 5120100% 451995% 381470% 24630% 12210% Percentile rank table

27. 27 0.5 1.52.53.54.55.5 cf = 0 cf = 2 cf = 6 cf = 14 cf = 19 cf = 20 x = 1 f = 2 x = 2 f = 4 x = 3 f = 8 x = 4 f = 5 x = 5 f = 1 Cumulative frequency chart

28. 28 xfcfc% 5120100% 451995% 381470% 24630% 12210% Percentile rank table 10% 30% 70% 95% 100% 0%.5 1.5 2.5 3.5 4.5 5.5

29. 29 6, 3, 7, 2, 8, 11, 6, 7, 16, 12, 9, 14, 8, 15, 9, 18, 7, 8, 21, 23 Number list

30. 30 xfcfc% 20-24220100% 15-1931890% 10-1431575% 5-9101260% 0-42210% Grouped percentile rank data table

31. 31 xfcfc% 20-24220 15-19318 10-14315 5-91012 0-422 24.5 19.5 14.5 9.5 4.5 0 100% 90% 75% 60% 10% 0% Interpolation data table

32. Scores 8 6 4 2 5-910-1415-1920-24 24.5 Frequency 0-4 19.5 1010 32 Simple Frequency distribution