Chapter 2: Frequency Distributions

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

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

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

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 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 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

Frequency Distribution Graphs 9

10 Scores Frequency Simple Frequency distribution

Scores Frequency Grouped frequency Distribution

Frequency Personality Type ABC Frequency vs. Personality type

13 Scores Frequency Simple Frequency distribution

Scores Frequency Frequency bar graph

Scores Frequency Grouped frequency Distribution

Scores Frequency Grouped frequency bar graph

Score f Score f xf Frequency vs. Percentages graphs xfp 51010/50= /50= /50= /50= /50=0.10

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% /400=0.4040% 34040/400=0.1010% 28080/400=0.2020% 14040/400=0.1010% N=50 N=400 Data tables showing percentages

19 Normal distribution of scores

IQ scores Relative frequency IQ score distribution

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

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

23 ABCD HGF E Frequency Distributions

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 1.3, 5.2, 4.0, 4.2, 3.0, 2.1, 4.3, 2.9, , 3.9, 3.3, 3.1, 1.9, 3.4, 2.2, 2.9, , Numbers grouped by color

26 xfcfc% % % % 24630% 12210% Percentile rank table

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 xfcfc% % % % 24630% 12210% Percentile rank table 10% 30% 70% 95% 100% 0%

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

30 xfcfc% % % % % % Grouped percentile rank data table

31 xfcfc% % 90% 75% 60% 10% 0% Interpolation data table

Scores Frequency Simple Frequency distribution