# Data Analysis

Please see Excel file.

a. Compute the mean and standard deviation for the sample data

b. Using the mean and standard deviation computed in part 9a) as estimates of the mean and standard deviation of salary for the population of benefits managers with an annual salary between $55,000 and $71,000

c. Develop a histogram for the sample data. Compute software provides .97 as the measure of skewness. Does it appear reasonable to assume that the distribution of annual salary can be approximated by a bell-shaped distribution?

d. Assume that the distribution of annul salary is bell-shaped. Using the mean and standard deviation computed in part (a) as estimates of the mean and standard deviation of salary for the population of benefits managers, use the empirical rule to determine the percentage of benefits managers with an annual salary between $55,000 and $71,000. Compare your answer with the value computed in part (b).

e. Do the sample data contain any outliers?

43. This assignment must be done in Excel

New York Stock Exchange (NYSE) Chairman Richard Grasso and NYSE Board of Directors came under fire for the large compensation package being paid to Grasso. When it comes to salary plus bonus, Grasso's $8.5 million out-earned the top executives of all major financial services companies. The data that follow show total annual salary plus bonus paid to the top executives of 14 finacial services companies (the Wall street Journal, September 17, 2003) Data are in millions

Company Salary & Bonus Company Salary&Bonus

Aetna 3.5 Fannie Mae 4.3

AIG 6.0 Federal Home Loan 0.8

Allstate 4.1 Fleet Boston 1.0

American Express 3.8 Freddie Mac 1.2

Chubb 2.1 Mellon Financial 2.0

Cigna 1.0 Merrill Lynch 7.7

Citigroup 1.0 Wells Fargo 8.0

A. What is the median annual salary plus bonus paid to the top executives of the 14 financial service companies?

B. Provide a five-number summary

C. Should Grasso's $8.5 million annual salry plus bonus be considered an outlier for this group of top executives? Explain

D. Show a box plot.

57. A survey of subscribers to Fortuen magazine asked the following question: "How many of the last four issues have you read?" Suppose that the following frequency distribution summarizes 500 responses.

Number Read Frequency

0 15

1 10

2 40

3 85

4 350

_________________________

Total 500

63. Public transportation and the automobile are two methods an employee can use to get to work each day. Sample of times recorded for each method are shown. Times are in minutes.

Public transportation 28 29 32 37 33 25 29 32 41 34

Automobile 29 31 33 32 34 30 31 32 35 33

A. Compute the sample mean time to get to work for each method.

B. Compute the sample standard deviation for each method

C. On the basis of your results from parts (a) and (b), which method of transportation should be preferred? Explain

D. Develop a box plot for each method. Does a comparison of the box plots support your conclusion in part (c)?

***See attached file for full problem description.***

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#### Solution Preview

33. Please see excel file Wageweb.

a. Compute the mean and standard deviation for the sample data.

The mean is the sum of the data (1890.1) divided by the number of cases (30). The standard deviation is calculated as the square root of the sum of the squared differences between each case and the mean, divided by the number of cases:

For this data set, the mean is 63.003, and the standard deviation is 4.002. These numbers were calculated in Excel.

b. Using the mean and standard deviation computed in part 9a) as estimates of the mean and standard deviation of salary for the population of benefits managers with an annual salary between $55,000 and $71,000.

I don't have question 9a. Even if I did, I don't understand this question (it's not even a complete sentence!).

I do have an idea about what this question might mean...

If the data is distributed normally, then 68.27% of the observations lie within 1 standard deviation of the mean. The percentage increases to 95.45% and 99.73% for 2 and 3 standard deviations, respectively.

So, 68.27% of salaries are between $59,001 and $67,005; 95.45% are between $54,999 and $71,007; and 99.73% are between $50,997 and $75,009. Therefore, I think the answer to this question is 95.45%.

Alternatively, we could just look at the sample and use the percentage of people with a salary between $55,000 and $71,000 in the sample as an estimate of the percentage of people in the entire population with a salary in that range.

There are 28 people in the sample with a salary between $55,000 and $71,000. This is 28/30 = 93.3% of the sample.

c. Develop a histogram for the sample data. Compute software provides .97 as the measure of skewness. Does it appear reasonable to assume that the distribution of annual salary can be approximated by a bell-shaped distribution?

The ...