You are examining the return on equity ratios of the nation's publicly owned companies. You wish to calculate a typical deviation from the average ROE, but you do not have time to gather data on all the firms. What measure should you use?
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A. B. C. D.D
A typical deviation is going to be a standard deviation, not a variance. When using a sample, instead of the entire population, you have sample standard deviation, not population standard deviation.
To calculate a measure of typical deviation from the average return on equity (ROE) without gathering data on all the firms, you should use the sample standard deviation, which is represented by option D.
The terms "population" and "sample" refer to the entire set of data and a subset of that data, respectively. In this case, you are examining the return on equity ratios of the nation's publicly owned companies, which would likely consist of a large number of firms. Gathering data on all these firms may be time-consuming and impractical, so you can use a sample to estimate the characteristics of the population.
The sample standard deviation measures the dispersion or variability of data within a sample. It provides an estimate of how much the individual data points deviate from the average value (mean) of the sample. The formula for calculating the sample standard deviation is slightly different from the formula for the population standard deviation, as it accounts for the fact that you are working with a sample rather than the entire population.
Option D, the sample standard deviation, is appropriate because it allows you to estimate the variability of the ROE ratios based on a subset of the data, which saves time compared to gathering data on all the firms. This measure will provide you with an understanding of how much individual firms' ROE ratios deviate from the average ROE in the sample.
Options A, B, and C refer to measures that are calculated using the entire population data. Since you do not have data on all the firms, it would be inaccurate to use these measures in this scenario.
To summarize, when you want to estimate the typical deviation from the average ROE without collecting data on all the firms, you should use the sample standard deviation (option D). It provides an estimate of variability based on a subset of the data and is appropriate when working with a sample rather than the entire population.