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

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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

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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:

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this