# Range - Managerial Economics

The simplest and most commonly employed measure of dispersion is the sample range, or the difference between the largest and smallest sample observations. In the telecommunications services example, the sample range in net profit is defined by the $7.6 million earned in the most profitable sample market to the$2.9 million earned in the least profitable sample observation. Note the very high degree of dispersion in net profits over the sample. The highest level of firm profits earned is more than two and one-half times, or 150 percent, greater than the lowest profit level. The range in net profit margin, though substantial, is much lower because these data are implicitly size-adjusted. The 16.4 percent earned in the market with the highest net profit margin is only 34 percent greater than the 12.2 percent margin earned in the market with the lowest profit margin. Profit variation is much less when one explicitly controls for firm size differences. As might be expected, the range in market size as measured by sales revenue is substantial. The $49.7 million in sales revenue earned in the largest market is roughly 150 percent greater than the$20.3 million size of the smallest market in the sample. Range has intuitive appeal as a measure of dispersion because it identifies the distance between the largest and smallest sample observations. Range can be used to identify likely values that might be associated with “best case” and “worst case” scenarios. Although range is a popular measure of variability that is easy to compute, it has the unfortunate characteristic of ignoring all but the two most extreme observations. As such, the range measure of dispersion can be unduly influenced by highly unusual outlying observations. The effects of outlyers are sometimes minimized by relying on interquartile or percentile range measures. For example,

the interquartile range identifies the spread that bounds the middle 50th percent of sample observations by measuring the distance between the first and third quartiles. Similarly, by measuring the distance between the 90th and 10th percentile of sample observations, the bounds on the middle 80 percent of sample observations can be determined. Both interquartile and percentile range measures are attractive because they retain the ease of calculation and intuitive appeal of the range measure of dispersion. However, like any range measure, they do not provide detailed information on the degree of variation among all sample observations. For this reason, range measures are often considered in conjunction with measures of dispersion that reflect the average deviation among all sample observations.