Getting to know the range, interquartile range, and standard deviation
The three most important measures of dispersion are defined as follows:-
The range is the difference between the highest score and the lowest score in a variable. These are the values that have been scored by participants in the study, and not necessarily the highest and lowest possible scores.
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The interquartile range is the difference between the upper quartile and the lower quartile in a set of ordered scores. Quartiles are formed by dividing a set of ordered scores into four equal-sized groups.
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The standard deviation (often abbreviated to Std. Dev. or SD) is the average deviation of scores in your data set from their mean score for a particular variable. The mean score is the average of scores on a variable. The standard deviation indicates the extent to which the scores on a variable deviate from the mean score.
Working out which measure of dispersion to use
You determine the most appropriate measure of dispersion as follows, depending on the nature of your data:-
Data measured at the nominal level: Because all three measures of dispersion require data to be ranked or summed, none of them are appropriate for data measured at the nominal level.
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Data measured at the ordinal level: The range and interquartile range are appropriate. The interquartile range is usually preferable, as it is more informative than the range.
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Data measured at the interval/ratio level: All three measures of dispersion we have examined are appropriate. The standard deviation is usually preferable. However, the standard deviation (or variance) isn’t appropriate when there are extreme scores and/or skewness in your data set. In this situation the interquartile range is usually preferable.