Median is the middle observation, sometimes has the potential to provide a measure of central tendency that is more useful than the sample mean. When the number of sample observations either above or below the mean is unusually large, then the sample mean can be far different from the value for a typical observation. Such divergences exist whenever a sample includes values that are either very small or very large in relation to the typical observation. For example, annual sales revenue can range from a few million dollars per year for small- to medium-size regional competitors into the tens of billions of dollars per year for large multinational corporations such as ExxonMobil, GE, or IBM. Despite the fact that the overwhelming majority of firms in most industries are relatively small, the average level of sales per firm can be relatively high—given the influence of revenues generated by industrial giants. Not only sales revenue but also profit numbers, wealth, and many other types of important economic data tend to be skewed. It is typical to find most observations at relatively modest levels of revenue, profit, or wealth; a small and declining number can be found along a diminishing “tail” that reaches upward to the end of the sample distribution. In such instances, the sample median can provide a very useful indicator of central tendency.
To illustrate, Table presents the net profit, profit margin, and sales revenue data contained in Table in a new rank order from largest to smallest values. Sample observations are now simply numbered from 1 to 25, because the values in any given row no longer refer to any single market. The sample average (and standard deviation discussed later) is not affected by this new sample ordering. In Table, sample medians for net profit, profit margin, and sales revenue can be determined by simply counting from the largest to the smallest values to find the middle observation. With an overall sample size of n = 25, the middle observation
occurs at the 13th sample observation, given exactly 12 larger and 12 smaller observations. For this sample of regional tele communications services markets, median net profit is $4.7 million, median profit margin is 14.9 percent, and median sales revenue is $32.8 million. Based on the sample median criterion, each of these observations is typical of sample values.
Sample averages for both net profit and sales revenue are slightly biased or skewed
upward because sample mean values are somewhat above median levels. This reflects the fact that a few very large regional markets can cause sample average values to be greater than the typically observed level. As discussed earlier, differences between sample means and medians are to be expected for much economic data given the long upward “tail” provided by the giants of industry. However, there is no necessary reason to suspect any relation between profit margins and firm size. Profit margins are net profit as a percentage of sales revenue. Because sales revenue is a commonly used measure of firm size, profit margin data are an example of “normalized” or size-adjusted data. The sample average profit margin of 14.8 percent is very close to the sample median of 14.9 percent. This indicates that the distribution of profit margin data is fairly centered around the sample mean observation, as is often the case when “normalized” or size-adjusted data are considered. There is, however, substantial variation around
the sample averages for net profit, profit margin, and sales revenues, and the chance of atypical sample values is correspondingly high.
Sample Rank Order of Annual Net Profit, Profit Margin, and Sales Revenue in 25 Regional Tele communications Services Markets
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Managerial Economics Tutorial
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