Return on Equity Ratios of Commercial Airlines | Population Variance Calculation

What is the Population Variance of Return on Equity (ROE) in the Commercial Airlines Industry?

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Question

You are examining the return on equity ratios of the nation's commercial airlines. You have calculated the mean ROE to be 8%, and the sum of the squared ROEs is 0.27. Assuming there are 30 commercial airlines, what is the population variance of ROEs in this industry?

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The population variance is equal to the sum of the squared differences between each population member and the population mean, divided by the number of items in the population. There is, however, an equivalent alternate formula that is more often used for large amounts of calculation. It is equal to the average squared observation less the squared mean. In this case, we have the average squared observation will be 0.27 / 30 = 0.009, less the squared mean of 8%. We have 0.009 - 0.0064 = 0.0026 = 26%%.

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