1. Chapter 2 EDRS 5305 Fall 2005

2. Descriptive Statistics  Organize data into some comprehensible form so that any pattern in the data can be easily seen and communicated to others

3. Frequency Distribution  An organized tabulation of the number of individual scores located in each category on the scale of measurement.

4. Frequency Distritbutions (cont.)  Organizes data  From highest to lowest  Grouping  Allows the researcher to see “at a glance” all of the data  Allows the researcher to see a score relative to all the other scores  By adding the frequencies, you can determine the number of scores or individuals

5. Example 2.1 N=20 8, 9, 8, 7, 10, 9, 6, 4, 9, 8, 7, 8, 10, 9, 8, 6, 9, 7, 8, 8

6. Xf 102 95 87 73 62 50 41 Ef=20 Ef=N EX=158 EX 2 =1288

7. Proportions and Percentages  There are other measures that describe the distribution of scores that can be incorporated into the table  Proportion  Percentage

8. Proportion  Measures the fraction of the total group that is associated with each score  Example 2.1  2 out of the 20 individuals scored a 6  Proportion  2/20 = 0.10  Proportion = p = f/N

9. Proportions (cont.)  Proportions are called relative frequencies  Because they describe the frequency (f) in relation to the total number (N)

10. Percentages  Distribution can also be described as percentages  Example 15% of the class earned an A  To compute:  Find the proportion (p)  Multiply by 100  Percentage = p(100) = f (100) N

11. Xf 102 95 87 73 62 50 41p=f/N%=p(100) 2/20 = 0.10 10% 5/20 = 0.25 25% 7/20 = 0.35 35% 3/20 = 0.15 15% 2/20 = 0.10 10% 0/20 = 0 0% 1/20 = 0.05 5%

12. Grouped Frequency Distribution Table  Can show groups of scores instead of each score individually  Example 90-100 5 scores  These groups or intervals are called class intervals

13. Guidelines for Grouped Frequency Distribution Tables  Should have about 10 class intervals  Width of each interval should be a relatively simple number  Count by 10s or 5s, etc.  Each class interval should start with a score that is a multiple of the width  10, 20, 30, etc.  All intervals should be the same width

14. Example 2.3 82, 75, 88, 93, 53, 84, 87, 58, 72, 94, 69, 84, 61, 91, 64, 87, 84, 70, 76, 89, 75, 80, 73, 78, 60

15. Steps  Determine range of scores  X=53 lowest  X=94 highest

17. Table 2.1 A grouped frequency distribution table Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning

18. Histograms  A picture of the frequency distribution graph  A vertical bar is drawn above each score  The height of the bar corresponds to the frequency  The width of the bar extends to the real limits of the score  A histogram is used when the data are measured on an interval or a ratio scale

20. Figure 2.1 A frequency distribution histogram Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning

22. Bar Graphs  When presenting the frequency distribution for data from a nominal or an ordinal scale, the graph is constructed so that there is some space between the bars  The bars emphasize that the scale consists of separate, distinct categories.

23. Figure 2.3 A bar graph Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning

25. Figure 2.4 A frequency distribution polygon Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning

26. Relative Frequencies and Smooth Curves  Sometimes the population is too big to construct a frequency distribution so researchers obtain frequencies from the entire group  Draw frequencies using relative frequencies (proportions) on the vertical axis.  Create a smooth curve

28. Figure 2.6 IQ scores from a normal distribution Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning

30. Shape of Frequency Distribution  Three characteristics that completely describe any distribution  Shape  Central Tendency  Variability

31. Shape  Nearly all distributions can be classified as being either symmetrical or skewed  Symmetrical  Skewed  Tail  Positively skewed  Negatively skewed

32. Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning Figure 2.8 Examples of different shapes for distribution