PART I: APPLICATION
Directions: Please answer each of the following questions (responses should be at least two paragraphs in length and be written in complete sentences, if applicable). Show essential calculations, if applicable.
1. The weights (in kilograms) of a group of crates being shipped to Panama are 95, 103, 110, 104, 105, 112, and 92. What is the mean deviation?
2. A sample of assistant professors on the business faculty at state-supported institutions in Ohio revealed the mean income to be $72,000 for 9 months with a standard deviation of $3,000. Using Chebyshev's Theorem, what proportion of the faculty earns more than $66,000 but less than $78,000?
3. A population consists of all the weights of all defensive tackles on Sociable University's football team. They are: Johnson, 204 pounds; Patrick, 215 pounds; Junior, 207 pounds; Kendron, 212 pounds; Nicko, 214 pounds; and Cochran, 208 pounds. What is the population standard deviation (in pounds)?
4. A study conducted by the Toledo police at the intersection of Byrne and Heather for the 7 to 9 AM drive time revealed the following number of vehicles proceeded through the intersection after the light changed. The information reported below is for a sample of seven days during a six month period: 6, 12, 7, 12, 8, 4, 5.
a. Compute the range.
b. Compute the sample mean.
c. What is the median?
d. What is the mode?
5. According to the Empirical Rule, what proportion of the customers pump between 8.00 gallons and 11.00 gallons?
6. The Canal Corporation recorded the last five annual percent changes in profit. What is the mean annual percentage change over the last five years?
|
8.4%
|
9.2%
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5.5%
|
10.2%
|
6.2%
|
7. Cook County public safety monitors the number of "driving on the influence" arrests and is interested in the distribution of arrests in the month of December over the last 5 years. The data are in the following chart. What is the standard deviation?
8. The mean monthly income of a group of college students is $500; the standard deviation is $20. According to Chebyshev's theorem, at least what percent of the incomes will lie between $400 and $600?
9. A sample of five full service gasoline stations, each carrying three grades of gasoline, was taken and the price per liter (to the nearest cent) was recorded for each grade of gasoline, as shown in the table below. What is the modal price of Unleaded gas?
|
Gasoline
|
1
|
2
|
3
|
4
|
5
|
|
Unleaded
|
$2.27
|
$2.27
|
$2.27
|
$2.27
|
$2.27
|
|
Unleaded plus
|
2.36
|
2.37
|
2.38
|
2.39
|
2.40
|
|
Super Unleaded
|
2.47
|
2.49
|
2.50
|
2.55
|
2.59
|
10. A sample of five full service gasoline stations, each carrying three grades of gasoline, was taken and the price per liter (to the nearest cent) was recorded for each grade of gasoline, as shown in the table below. What is the median price of Super Unleaded gas?
|
Gasoline
|
1
|
2
|
3
|
4
|
5
|
|
Unleaded
|
$2.27
|
$2.27
|
$2.27
|
$2.27
|
$2.27
|
|
Unleaded plus
|
2.36
|
2.37
|
2.38
|
2.39
|
2.40
|
|
Super Unleaded
|
2.47
|
2.49
|
2.50
|
2.55
|
2.59
|
PART II: CASE STUDY
Directions: Please conduct the following case study. You will work on this case study for Modules 1 through 8.
For your Module 2 Case Study, you created some dummy data values related to your business problem or issue of interest. Using these values, which measure(s) of centrality can you compute or determine for these values and why? What do they tell us about your data?
What would a business decision maker conclude from these values of centrality? How might he/she use them to address the business issue that you have identified?
PART III: JOURNAL ACTIVITY
Please identify one key concept from this module that you find particularly challenging or relevant to your interests. Write a short paper (2 to 3 pages) explaining it in greater depth. Remember to cite your sources. Please visit the Academic Resource Center (ARC) for concise guidelines on APA format.