Exam 3: Numerical Summaries of Center and Variation

Based on the boxplot for the West, which of the following is true?

Choose the most appropriate measure of center then calculate the typical value rounded to the nearest tenth.

The following nine values represent race finish times in hours for a randomly selected group of participants in an extreme 10k race (a 10k race with obstacles). Which of the following is closest to the mean of the following data set?

Use the following information to answer the question. The economic impact of an industry, such as sport fishing, can be measured by the retail sales it generates. In 2006, the economic impact of great lakes fishing in states bordering the great lakes had a mean of $318 and a standard deviation of $83.5. Note that all dollar amounts are in millions of dollars. Assume the distribution of retail sales is unimodal and symmetric. (Source: National Oceanic and Atmospheric Administration). -For what percentage of great lakes states would you expect the economic impact from fishing to be between $234.5 and $401.5 (in millions of dollars)?

Using the boxplot for the West, determine which of the following statements about the distribution cannot be justified.

Use the following information to answer the question. The economic impact of an industry, such as sport fishing, can be measured by the retail sales it generates. In 2006, the economic impact of great lakes fishing in states bordering the great lakes had a mean of $318 and a standard deviation of $83.5. Note that all dollar amounts are in millions of dollars. Assume the distribution of retail sales is unimodal and symmetric. (Source: National Oceanic and Atmospheric Administration). -If a new report came out saying that the economic impact of great lakes sport fishing on the economy of Illinois was $93,588,546, would you say this was unusual? Note that this dollar amount must be converted before calculating a standard score.

Use the following information to answer the question. A junior high gym teacher recorded the time, in minutes, that it took two of her classes to run one mile. Here are the summary statistics for each class: Class A: x = 9.6, s = 1.1 Class B: x = 9.9; s = 1.5 -Calculate the sample variance for each class. Round to the nearest hundredth and be sure to use the correct symbols and units.

Use the following information to answer the question. The average snowfall for cities in Michigan is 71.6 inches with a standard deviation of 9.7 inches. Assume the distribution for annual snowfall is approximately unimodal and symmetrical. -In 2007, the annual snowfall in Grand Rapids, Michigan was 97.2 inches. What is the standard score for the 2007 snowfall? Was this an unusual amount of snowfall for a city in Michigan? Show all work and round any calculations to the nearest tenth.

In your own words, explain what the Empirical Rule says and what conditions a distribution must meet in order to apply the rule.

The average grade on an algebra exam was 76% with a standard deviation of 6 percentage points. The average grade on a chemistry exam was 81% with a standard deviation of 2 percentage points. Julie got a grade of 83% on both exams. Which exam did she do relatively better on? Show all work and round any calculations to the nearest hundredth.

Use the following information to answer the question. Here is a table recording the number of deaths for the top thirteen worst U.S. tornados since 1925. A histogram showing the distribution is also included. -The worst tornado on record since 1925 is a tornado that went through Missouri, Illinois, and Indiana on March 18, 1925. It killed 689 people. Suppose that when this value was entered into a calculator or other software a mistake was made and it was entered as 1,689. Choose the statement that describes what affect this mistake will have on the median and the mean.

Use the following information to answer the question. Data and summary statistics about college professor's salaries was gathered from nine institutions and is presented below. This salary information is from professors teaching at the Master's level. Men: x = 67691; s = 14506 Women: x = 65323; s = 13274 -According to a national study, the average salary for a professor teaching at the Master's level is approximately $70,000. How does the data from these nine institutions compare to this? Does it appear that salaries for either group at these nine institutions agrees or disagrees with the study?

Use the following information to answer the question. The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses' ages is approximately unimodal and symmetric. -Between what two values would you expect to find about 95% of the lead actresses ages?

The following list shows the age at appointment of U.S. Supreme Court Chief Justices appointed since 1900. Use the data to answer the question. -Find the mean, rounding to the nearest tenth of a year, and interpret the mean in this context.

Use the following information to answer the question. The economic impact of an industry, such as sport fishing, can be measured by the retail sales it generates. In 2006, the economic impact of great lakes fishing in states bordering the great lakes had a mean of $318 and a standard deviation of $83.5. Note that all dollar amounts are in millions of dollars. Assume the distribution of retail sales is unimodal and symmetric. (Source: National Oceanic and Atmospheric Administration). -If a new report came out saying that the economic impact of great lakes sport fishing on the economy of Illinois was $93,588,546, would you say this was unusual? Note that this dollar amount must be converted before calculating a standard score.

Use the following information to answer the question. Data and summary statistics about college professor's salaries was gathered from nine institutions and is presented below. This salary information is from professors teaching at the Master's level. Men: x = 67691; s = 14506 Women: x = 65323; s = 13274 -Which group has more variability? How would this affect the histogram for the group, compared to the other group? Explain.

Use the following data to answer the question. Here are the scores on a recent statistics midterm exam (Scores have been listed from lowest to highest). A histogram showing the distribution is also included. -Choose the most appropriate measure of variability for the data and calculate it. Explain why you chose the measure of variability that you did. Round all calculations to the nearest tenth if necessary.

A city planner says, "The typical commute to work for someone living in the city limits is less than the commute to work for someone living in the suburbs." What does this statement mean?

Use the following information to answer the question. The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses' ages is approximately unimodal and symmetric. -In 2010, popular actress Jennifer Aniston was 41- years- old. What is Jennifer Aniston's age if it is standardized? Would it be unusual for a 41- year- old actress to be in a top- grossing film of 2010? Assume the Empirical Rule applies and round to the nearest hundredth.

In 2007, the mean price per pound of lobster in New England was $11.48 and the standard deviation was $2.12. A histogram of the data shows that the distribution is symmetrical. A local New England grocer is selling lobster for $8.99 per pound. What is this price in standard units? Assuming the Empirical Rule applies, would this price be considered unusual or not? Round to the nearest hundredth.