Question 1

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

Accepted Answer

The median is the most appropriate measure of center when the data set is skewed or has outliers, and the typical value is 181.0.

Question 2

A school board member says, "The typical bus ride to school for a student living in the city limits is more than the bus ride to school for a student living in the suburbs." What does this statement mean?

Accepted Answer

The statement implies that the average or median bus ride time for students living in the city is longer than that for students living in the suburbs.

Question 3

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

Accepted Answer

Median is the most appropriate measure of center for a skewed distribution.

Question 4

Calculate the five- number summary for the following dataset.

Accepted Answer

The answer of Calculate the five- number summary for the...

Question 5

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).
-The economic impact of fishing for nearly all great lakes states should fall within what range (in millions of dollars)?

Accepted Answer

The range for nearly all data in a unimodal and symmetric distribution (approximately 95%) is within two standard deviations from the mean. Therefore, the range is $318 ± 2($83.5), which is $151 to $485 million.

Question 6

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?

Accepted Answer

The answer of The following nine values represent race finish...

Question 7

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 $151.00 and $485.00 (in millions of dollars)?

Accepted Answer

The range $151 to $485 is within two standard deviations from the mean ($318 ± 2*$83.5). According to the empirical rule, about 95% of data falls within two standard deviations in a normal distribution.

Question 8

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.

Accepted Answer

The mean age of U.S. Supreme Court Chief Justices appointed since 1900 is calculated to be 61.4 years, which is the typical age at which they are appointed.

Question 9

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.
 
-The U.S. Supreme Court Chief Justice data was used to create the following output in an Excel spreadsheet. Choose the statement that best summarizes the variability of the dataset.

Accepted Answer

The answer of The following list shows the age at...

Question 10

Calculate the five- number summary for the following dataset. 41.19, 83.51, 19.98, 114.60, 63.08, 83.88

Accepted Answer

The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. For the dataset, these are 19.98, 41.19, 73.295, 83.88, and 114.6 respectively.

Question 11

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 68% of the lead actresses ages?

Accepted Answer

The empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation of the mean. In this case, the mean is 29.6 years and the standard deviation is 6.35 years. So, we would expect to find about 68% of the lead actresses ages between 29.6 - 6.35 = 23.25 years and 29.6 + 6.35 = 35.95 years.

Question 12

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).
-The economic impact of fishing for nearly all great lakes states should fall within what range (in millions of dollars)?

Accepted Answer

The answer of Use the following information to answer the...

Question 13

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.

Accepted Answer

The answer of Use the following information to answer the...

Question 14

Use the following information to answer the question. The mean age of lead actors from the top ten grossing movies of 2007 was 36.4 years with a standard deviation of 9.87 years. Assume the distribution of the actors ages is approximately unimodal and symmetric.
-In 2007, popular actor and singer Justin Timberlake was 26- years- old. What is Justin Timberlake's age in 2007 if it is standardized? Would it be unusual for a 26- year- old actor to be in a top- grossing film of 2007? Assume the Empirical Rule applies and round to the nearest hundredth.

Accepted Answer

Justin Timberlake's age is 26 years old, which is 10.4 years below the mean. The standardized score is (26 - 36.4) / 9.87 = -1.05. According to the Empirical Rule, about 68% of the data falls within one standard deviation of the mean, so it would not be unusual for a 26-year-old actor to be in a top-grossing film of 2007.

Question 15

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 mean and median.

Accepted Answer

The median is not affected by extreme values, so it will not be affected by the error. The mean, however, is affected by extreme values, so it will be higher than it should be.

Question 16

Below is the standard deviation for extreme 10k finish times for a randomly selected group of women and men. Chose the statement that best summarizes the meaning of the standard deviation.

Accepted Answer

The answer of Below is the standard deviation for extreme...

Question 17

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

Accepted Answer

The answer of Using the boxplot for the Midwest, determine...

Question 18

Pick the statement that best describes the shape of the distribution for the states in the West.

Accepted Answer

The statement describes a distribution that is right-skewed, which means it has a longer tail on the right side, and mentions the presence of a possible outlier, which is a common characteristic of right-skewed distributions.

Question 19

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

Accepted Answer

25% of the states sentenced more than 15,706 prisoners, as indicated by the upper quartile in the boxplot.

Question 20

Pick the statement that best describes the shape of the distribution for the states in the Midwest.

Accepted Answer

The answer of Pick the statement that best describes the...

Quiz 3: Numerical Summaries of Center and Variation