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Chapter 3

Data Analysis Chapter 3.docx

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Chapter 3: Frequency Distributions  A frequency distribution- presents the score values and their frequency of occurrence. When presented in a table, the score values are listed in rank order, with the lowest score value usually at the bottom of the table. o The major purpose of frequency distributions is to present the scores in such a way to facilitate ease of understanding and interpretation. o When there are many scores and the score range widely listing individual scores results in many values with a frequency of zero and a display fro which it is difficult to visualize the shape of the distribution and its central tendency. Under these conditions, the individual scores are usually grouped into class intervals and presented as a frequency distribution of grouped scores.  The larger the interval used, the greater the ambiguity. Constructing a Frequency Distribution of Grouped Scores 1. Find the range of the 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 value at the bottom. 4. Tally the raw scores into the appropriate class intervals. 5. Add the tallies for each interval to obtain the interval frequency. Relative Frequency, Cumulative Frequency, and Cumulative Percentage Distributions  Relative Frequency Distribution- indicates the proportion of the total number of scores that occurs in each interval.  To convert a frequency distribution into a relative frequency distribution, the frequency for each interval is divided by the total number of scores. Thus, Relative ƒ=  Cumulative Frequency Distribution- indicates the number of scores that fall below the upper real limit of each interval.  The cumulative frequency for each interval is found by adding the frequency of that interval to the frequencies of all the class intervals below it.  Cumulative Percentage Distribution- indicates the percentage of scores that fall below the upper real limit of each interval.  The cumulative percentage for each interval is found by converting cumulative frequencies to cumulative percentages as follows: cum%= Percentiles  Percentiles are measures of relative standing. They are used extensively in education to compare the performance of an individual to that of a reference group. A percentile or percentile point is the value on the measurement scale below which a specified percentage of the scores in the distribution fall. Computation of Percentile Points  Ex. Find the 50th percentile point (P ) fo50the exam scores in table 3.8 on page 56. P is the scale value below which 50% of the scores fall (therefore if 50 there are 70 scores, it is the value below which 35 scores fall). To determine P 50thin an
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