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PSY 3204- Chapter 3

# PSY 3204- Chapter 3 - PSY 3204 CHAPTER 3 I Constructing...

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PSY 3204---- CHAPTER 3 I. Constructing Frequency Distributions A. A list of rank ordered scores and their frequency of occurrence in tabular form is called a frequency distribution. When the data is rank ordered, it is easier to understand. B. Grouping data . Individual scores are often grouped together into class intervals of equal width to allow one to visualize the shape of a distribution and its central tendency. This is called a frequency distribution of grouped scores. 1. Distributions are usually divided into 10 to 20 intervals. 2. If the intervals are too wide, too much information is lost; if too narrow, there are too many zero frequency intervals which distort the shape of the distribution. C. Constructing a frequency distribution of grouped scores. 1. Find the range of scores. 2. Determine the width of each class interval (i). 3. List the limits of each class interval, placing the interval containing the lowest score at the bottom. 4. Tally the raw scores into the appropriate class intervals. 5. Add the tallies to obtain the interval frequency. II. Desired Frequency Distributions . It is often desirable to express data in forms other than the basic frequency distribution. A. Relative frequency distribution . This indicates the proportion of the total number of scores that occurred in each interval. B. Cumulative frequency distribution . This indicates the number of scores which fell below the upper real limit of each interval. C. Cumulative percentage distribution . This indicates the percentage of scores which fell below the upper real limit of each interval. To convert cumulative frequencies to cumulative percentages one can apply the formula:

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cum % = (cum f)/N × 100 III. Measures of Relative Standing . These are used to compare performances of an individual to that of a reference group. A. Percentile point is the value on the measurement scale below which a specified percentage of scores in the distribution fall. B. Formula: Percentile Point = X L + ( i/f i )(cum f P - cum f L ) C. Percentile rank of a score is the percentage of scores lower than the score in question. D. Formula: IV. Graphing Techniques A. Graph characteristics. 1. A graph has two axes, the vertical is called the ordinate and the horizontal is called the abscissa. 2. Scores are shown on the abscissa; frequency is shown on the ordinate. 3. Graphs are generally 3/4 as high as they are long. B. Types of graphs for frequency distributions. 1. Bar graphs are generally used for nominal or ordinal data. The abscissa shows categories and the ordinate frequency. 2. Histograms are generally used for interval or ratio data. The abscissa shows the class interval for the data and the ordinate shows frequency. Vertical bars must touch each other. 3. Frequency polygons are similar to histograms, except that instead of using bars, a point is plotted over the midpoint of each interval at a height corresponding to the frequency of the interval. In addition, the line is extended to meet the horizontal axis at the midpoint of the two end- adjacent intervals.
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PSY 3204- Chapter 3 - PSY 3204 CHAPTER 3 I Constructing...

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