chp 3 instructor manual

# chp 3 instructor manual - Chapter 3 STATISTICAL ANALYSIS OF...

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Chapter 3 STATISTICAL ANALYSIS OF ECONOMIC RELATIONS QUESTIONS AND ANSWERS Q3.1 Is the mean or the median more likely to provide a better measure of typical sales revenue for companies included in the Fortune 500? Q3.1 ANSWER When the number of sample observations above or below the mean is unusually large, the sample median, or middle observation, has the potential to provide a better measure of central tendency that is more useful than the sample mean. Annual sales revenues range from only a few million dollars per year for small- to medium-size regional competitors into the tens of billions of dollars per year for large corporations. Despite the fact that the overwhelming majority of firms in most industries are relatively small, the average profit level per firm can be relatively high--given the influence of industrial giants. It is typical to find most observations at relatively modest levels of profit, although 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 is often preferred to the mean as an indicator of central tendency. Q3.2 What important advantage does the standard deviation have over the range measure of dispersion in company sales for firms in the computer software industry? Q3.2 ANSWER Range has intuitive appeal as a measure of dispersion because it clearly identifies the distance between the largest and smallest sample observations. As such, 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. Therefore, despite its obvious ease of calculation and intuitive interpretation, the usefulness of the range measure of dispersion is limited by its basic failure to reflect deviation throughout the sample or entire population. For this reason, range measures of dispersion are often supplemented by measures that reflect dispersion

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46 Chapter 3 through the sample or entire population such as the variance, or average squared deviation from the mean, and the standard deviation, or square root of the variance. Q3.3 If the average and median rate of return on equity for publicly-traded firms in a given industry is 15 percent, what does this imply about sample distribution? Q3.3 ANSWER If the mean and the median are the same, the sample is normally or uniformly distributed about the mean. The mean or average represents an especially attractive measure of central tendency when upward and downward divergences from the mean are fairly balanced. If the number of sample observations above the sample mean is roughly the same as the number of observations below the sample mean, then both
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