What are the big corporations doing with their wealth? One way to answer this qu

Question

What are the big corporations doing with their wealth? One way to answer this question is to examine profits as percentage of assets. A random sample of 50 Fortune 500 companies gave the following information. (Source: Based on information from Fortune 500, Vol. 135, No. 8.) Estimate the sample mean, sample variance, and sample standard deviation for profit as percentage of assets. (Enter your answers to one decimal place.)

Explanation / Answer

Understanding this question is the hardest part of this problem. We have 15 companies with a net profit (as a percentage of assets between 8.5 and 12.5, 16 companies with net profit between 12.6 and 16.5, 7 companies with net profits between 16.6 and 20.5, 7 companies with net profits between 20.6 and 24.5, and 5 companies between 24.6 and 28.5.

We will assume the average for the first group (8.5-12.5) is (8.5 + 12.5)/2 = 21/2 = 10.5

Average the limits and multiplying by the number of companies.

15 * (8.6+12.5)/2 = 157.5
16 * (12.6+16.5)/2 = 232.8
7 * (16.6+20.5)/2 = 101.85
7 * (20.6+24.5)/2 = 115.25
5 * (24.6+28.5)/2 = 132.75

Mean = (157.5+232.8+101.85+115.25+132.75)/50 = 740.15/50 = 14.803

For sample variance, used the mean calculated above. Take the sum of the squared differences, multiply by the number of companies in the category and then divide by 50 (number of companies).

For the standard deviation, take the square root of the variance.

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