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FREQUENCY DISTRIBUTION

They indicate how values in a sample are dis-persed around the mean. These measures provide information about the data that is not available from measures of central tendency. They indicate how different the scores are—the extent to which individual values deviate from one another. If the individual values are similar, measures of variability are small and the sample is relatively homogeneous in terms of those values. Heterogeneity (wide variation in scores) is important in some statistical procedures, such as correlation. Heterogeneity is determined by measures of variability. The measures most commonly used are range, difference scores, variance, and SD (see Exercise 9 ). FIGURE 27-1 ■ FREQUENCY DISTRIBUTION OF YEARS OF BIOLOGIC USE, WITHOUT OUTLIER AND WITH OUTLIER. 0FrequencyFrequency3-3.90-0.92-2.91-1.94-4.93-3.90-.91-1.92-2.94-4.95-5.96-6.97-7.98-8.99-9.910-10.911-11.9Years of biologic useYears of biologic use3.02.52.01.51.00.503.02.52.01.51.00.5 294EXERCISE 27 • Calculating Descriptive StatisticsCopyright © 2017, Elsevier Inc. All rights reserved. Range The simplest measure of dispersion is the range . In published studies, range is presented in two ways: (1) the range is the lowest and highest scores, or (2) the range is calculated by subtracting the lowest score from the highest score. The range for the scores in Table 27-1 is 0.3 and 4.0, or it can be calculated as follows: 4.0 − 0.3 = 3.7. In this form, the range is a difference score that uses only the two extreme scores for the comparison. The range is generally reported but is not used in further analyses. Difference Scores Difference scores are obtained by subtracting the mean from each score. Sometimes a difference score is referred to as a deviation score because it indicates the extent to which a score deviates from the mean. Of course, most variables in nursing research are not “scores,” yet the term difference score is used to represent a value ’ s deviation from the mean. The difference score is positive when the score is above the mean, and it is negative when the score is below the mean (see Table 27-2 ). Difference scores are the basis for many statistical analyses and can be found within many statistical equations. The formula for difference scores is: XX− Σof absolute values95:. TABLE 27-2 DIFFERENCE SCORES OF DURATION OF BIOLOGIC USE X –X XX– 0.1 − 1.9 − 1.80.3 − 1.9 − 1.61.3 − 1.9 − 0.61.5 − 1.9 − 0.41.5 − 1.9 − 0.42.0 − 1.90.12.2 − 1.90.33.0 − 1.91.13.0 − 1.91.14.0 − 1.92.1 The mean deviation is the average difference score, using the absolute values.

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