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.)

Profit as percentage of assets 8.6-12.5 12.6-16.5 16.6-20.5 20.6-24.5 24.6-28.5
Number of companies 15 18 4 3 10

Step-by-step explanation:

For this case is useful construct the following table:

Class          Midpoint (xi)    fi         xi* fi        xi^2* fi

_________________________________________

8.6-12.5         10.55           15      158.25     1669.538

12.6-16.5        14.55           18      261.9       3810.645

16.6-20.5       18.55            4       74.2        1376.41

20.6-24.5      22.55           3       67.65      1525/508

24.6-28.5      26.55           10      265.5     7049.025

_________________________________________

Total                                  50     827.5       15431.13

For this case the sample mean can be calculated with this formula:

And if we replace we got:

For the sample variance we can ise the following formula:

And replacing we got:

And for the deviation we just take the square root of the variance and we got:

ou would have 12 of each