Chapter 2 EDRS 5305 Fall 2005

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

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

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

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

Xf Ef=20 Ef=N EX=158 EX 2 =1288

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

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

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

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

Xf p=f/N%=p(100) 2/20 = % 5/20 = % 7/20 = % 3/20 = % 2/20 = % 0/20 = 0 0% 1/20 = %

Grouped Frequency Distribution Table  Can show groups of scores instead of each score individually  Example scores  These groups or intervals are called class intervals

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

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

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

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

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

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

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.

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

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

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

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

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

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

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