What is the purpose of the range, and how is it determined in a distribution of scores?
Measures of dispersion, or measures of variability, are descriptive statistical techniques conducted to identify individual differences of the scores in a sample. These techniques give some indication of how scores in a sample are dispersed, or spread, around the mean. The measures of dispersion indicate how different the scores are or the extent that individual scores deviate from one another. If the individual scores are similar, dispersion or variability values are small and the sample is relatively homogeneous, or similar, in terms of these scores. A heterogeneous sample has a wide variation in the scores, resulting in increased values for the measures of dispersion. Range and standard deviation are the most common measures of dispersion included in research reports.
The simplest measure of dispersion is the range. In published studies, range is presented in two ways: (1) the range includes the lowest and highest scores obtained for a variable, or (2) the range is calculated by subtracting the lowest score from the highest score. For example, the range for the following scores, 8, 9, 9, 10, 11, 11, might be reported as 8 to 11 (8–11), which identifies outliers or extreme values for a variable. The range can also be calculated as follows: 11 − 8 = 3. In this form, the range is a difference score that uses only the two extreme scores for the comparison. The range is generally reported in published studies but is not used in further analyses (Grove, Burns, & Gray, 2013).
The standard deviation (SD) is a measure of dispersion and is the average number of points by which the scores of a distribution vary from the mean. The SD is an important statistic, both for understanding dispersion within a distribution and for interpreting the relationship of a particular value to the distribution. When the scores of a distribution deviate from the mean considerably, the SD or spread of scores is large. When the degree of deviation of scores from the mean is small, the SD or spread of the scores is small. SD is a measure of dispersion that is the square root of the variance. The equation and steps for calculating the standard deviation are presented in Exercise 27, which is focused on calculating descriptive statistics.
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