 |  Statistics for the Behavioral Sciences, 4/e Michael Thorne,
Mississippi State University -- Mississippi State
Martin Giesen,
Mississippi State University -- Mississippi State
The Frequency Distribution
Chapter Overview| A first approach to organizing data is to arrange the numbers in order of value. By convention, we list the highest number first, followed by the next highest, and so on. The data can be condensed slightly by constructing a frequency distribution in which the scores are ranked from highest to lowest and the number of times each score occurs (its frequency) is listed beside it. Scores are symbolized by the letter X, whereas frequencies appear under the letter f.
A continuous variable is one whose measurement can take an infinite number of values; a discrete variable is one capable of assuming only specific values. Gaps in the measurement of a continuous variable are apparent rather than real; that is, the gaps are an artifact of the crudeness of measurement. Data from a continuous variable presented in the form of whole numbers have gaps between the numbers; these numbers with gaps are called apparent limits. Real limits close the gaps by subtracting a half unit from the lower apparent limit and adding a half unit to the upper apparent limit.
To compare frequency distributions from samples varying in size, we need to convert the frequencies to percentages; that is, we need to put them on an equivalent basis. The resulting distribution is called a percentage or relative frequency distribution. A cumulative frequency distribution is constructed by starting with the distribution's lowest interval and accumulating frequencies as you ascend. Thus, for any interval, the cumulative frequency tells the number of scores contained in that interval plus the sum of the frequencies in intervals below the one considered. Converting each of the accumulated frequencies to a percentage results in a cumulative percentage distribution. |
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2003 McGraw-Hill Higher Education