Question 1

The most frequently used measure of central tendency is:
A) median.
B) mean.
C) mode.
D) middle value.

Accepted Answer

The mean is the most frequently used measure of central tendency because it takes into account all values in the dataset, providing a comprehensive average.

Question 2

The distribution of dollars paid for car insurance by car owners in a major east coast city is bell- shaped with a mean equal to $750 every six months and a standard deviation equal to $100. Based on this information we should use Tchebysheff's theorem to determine the conservative percentage of car owners that will pay between $550 and $950 for car insurance.

Accepted Answer

Tchebysheff's theorem is applicable for any shape of distribution, not just bell-shaped distributions. For bell-shaped (normal) distributions, the Empirical Rule is more appropriate for estimating percentages within certain standard deviations from the mean.

Question 3

Which of the following statements is true?
A) The mean of a population will always be larger than the population standard deviation.
B) The mean of the population will generally be larger than the mean of the sample selected from that population.
C) The population mean and a sample mean for a sample selected from that population will usually be different values.
D) The population mean and sample mean will always be identical.

Accepted Answer

The population mean and a sample mean for a sample selected from that population will usually be different due to sampling variability, although they may be close if the sample is representative and large enough. Statements A, B, and D are not necessarily true and depend on specific circumstances.

Question 4

Acme Taxi has two taxi cabs. The manager tracks the daily revenue for each cab. Over the past 20 days, Cab A has averaged $76.00 per night with a standard deviation equal to $11.00. Cab B has averaged $200.00 per night with a standard deviation of $18.00. Based on this information, the coefficient of variation for Cab B is 9 percent.

Accepted Answer

The coefficient of variation is a measure of relative variability. It is calculated by dividing the standard deviation by the mean. For Cab B, the coefficient of variation is 18 / 200 = 0.09, or 9%.

Question 5

Suppose a distribution has a mean of 80 and standard deviation of 10. It is found that 84 percent of the values in the data set lie between 70 and 90. This implies that the distribution is not bell-shaped.

Accepted Answer

A bell-shaped distribution, or normal distribution, typically has about 68% of the data within one standard deviation from the mean. Here, 84% within one standard deviation suggests a different distribution shape.

Question 6

The distribution of bankcard balances for customers is highly right-skewed with a mean of $1,100 and a standard deviation equal to $250. Based on this information, approximately 68 percent of the customers will have bank balances between $850 and $1,350.

Accepted Answer

The rule that approximately 68% of observations fall within one standard deviation of the mean (the empirical rule) applies to normal or nearly normal distributions, not to highly skewed distributions.

Question 7

A population measure, such as the population mean, is called a:
A) statistic.
B) parameter.
C) prime number.
D) sample value.

Accepted Answer

A parameter is a numerical value that summarizes a characteristic of a population, such as the population mean.

Question 8

Acme Taxi has two taxi cabs. The manager tracks the daily revenue for each cab. Over the past 20 days, Cab A has averaged $76.00 per night with a standard deviation equal to $11.00. Cab B has averaged $200.00 per night with a standard deviation of $18.00. Based on this information, Cab B has the greatest relative variation.

Accepted Answer

Relative variation is calculated as the standard deviation divided by the mean. For Cab A, the relative variation is $11.00 / $76.00 ≈ 0.145. For Cab B, it is $18.00 / $200.00 = 0.09. Therefore, Cab A has the greater relative variation.

Question 9

Consider the following sample data:  For these data the sample mean is:
A) 8
B) 10
C) 3
D) 12

Accepted Answer

The answer of Consider the following sample data:  For...

Question 10

If a business manager selected a sample of customers and computed the mean income for this sample of customers, she has computed:
A) a statistic.
B) an ordinal value.
C) a nominal value.
D) a parameter.

Accepted Answer

A statistic is a characteristic of a sample, so when the business manager computes the mean income for a sample of customers, she is indeed calculating a statistic.

Question 11

The credit card balances for customers at State Bank and Trust has a mean equal to $800 and a standard deviation equal to $60.00. Kevin Smith's balance is $1,352. Based on this, his standardized value is 9.20.

Accepted Answer

The answer of The credit card balances for customers at...

Question 12

A small company has 7 employees. The numbers of years these employees have worked for this company are shown as follows:  Based upon this information, the median number of years that employees have been with this company is:
A) 9 years.
B) 16 years.
C) 10 years.
D) 14 years.

Accepted Answer

The answer of A small company has 7 employees. The...

Question 13

A small company has 7 employees. The numbers of years these employees have worked for this company are shown as follows:  Based upon this information, the mode number of years that employees have been with this company is:
A) 16
B) 2
C) 9
D) 10

Accepted Answer

The answer of A small company has 7 employees. The...

Question 14

Based on the empirical rule we can assume that all bell-shaped distributions have approximately 95 percent of the values within ± 2 standard deviations of the mean.

Accepted Answer

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean.

Question 15

A sample of people who have attended a college football game at your university has a mean = 3.2 members in their family. The mode number of family members is 2 and the median number is 2.0. Based on this information:
A) the population mean exceeds 3.2.
B) the distribution is bell-shaped.
C) the distribution is right-skewed.
D) the distribution is left-skewed.

Accepted Answer

Given that the mean (3.2) is higher than both the median and mode (both 2), the distribution is right-skewed. This indicates a longer tail on the right side of the distribution, where there are values (family sizes) that are significantly larger than the mode and median, pulling the mean upwards.

Question 16

A major automobile maker has two models of sedans. The first model has been shown to get an average of 27 mpg on the highway with a standard deviation equal to 5 mpg. The second model gets 33 mpg on average with a standard deviation of 8 mpg. Based on this information the first car model is relatively more variable than the second car model.

Accepted Answer

The coefficient of variation (CV), which is the standard deviation divided by the mean, is used to compare variability relative to the mean between datasets. For the first model, CV = 5 / 27. For the second model, CV = 8 / 33. The second model has a higher CV, indicating it is relatively more variable.

Question 17

Consider the following sample data:  For these data the median is:
A) 7.5
B) 3.5
C) 10
D) None of the above

Accepted Answer

The answer of Consider the following sample data:  For...

Question 18

Based on the empirical rule we can expect about 95 percent of the values in bell-shaped distributions to be within ± one standard deviation of the mean.

Accepted Answer

The empirical rule states that about 95 percent of the values in a bell-shaped distribution are within ± two standard deviations of the mean, not one.

Question 19

A small company has 7 employees. The numbers of years these employees have worked for this company are shown as follows:  Based upon this information, the mean number of years that employees have been with this company is:
A) 16
B) x
C) 8.40
D) 10

Accepted Answer

The answer of A small company has 7 employees. The...

Question 20

Consider a situation involving two populations where population 1 is known to have a higher coefficient of variation than population 2. In this situation, we know that population 1 has a higher standard deviation than population 2.

Accepted Answer

The coefficient of variation is a measure of relative variability that is calculated as the standard deviation divided by the mean. A higher coefficient of variation in population 1 compared to population 2 indicates that population 1 has greater variability relative to its mean, not necessarily a higher standard deviation in absolute terms.

Quiz 3: Describing Data Using Numerical Measures

The most frequently used measure of central tendency is:

Which of the following statements is true?

Suppose a distribution has a mean of 80 and standard deviation of 10. It is found that 84 percent of the values in the data set lie between 70 and 90. This implies that the distribution is not bell-shaped.

The distribution of bankcard balances for customers is highly right-skewed with a mean of $1,100 and a standard deviation equal to $250. Based on this information, approximately 68 percent of the customers will have bank balances between $850 and $1,350.

A population measure, such as the population mean, is called a:

Consider the following sample data: For these data the sample mean is:

If a business manager selected a sample of customers and computed the mean income for this sample of customers, she has computed:

The credit card balances for customers at State Bank and Trust has a mean equal to $800 and a standard deviation equal to $60.00. Kevin Smith's balance is $1,352. Based on this, his standardized value is 9.20.

A small company has 7 employees. The numbers of years these employees have worked for this company are shown as follows: Based upon this information, the median number of years that employees have been with this company is:

A small company has 7 employees. The numbers of years these employees have worked for this company are shown as follows: Based upon this information, the mode number of years that employees have been with this company is:

Based on the empirical rule we can assume that all bell-shaped distributions have approximately 95 percent of the values within ± 2 standard deviations of the mean.

A sample of people who have attended a college football game at your university has a mean = 3.2 members in their family. The mode number of family members is 2 and the median number is 2.0. Based on this information:

Consider the following sample data: For these data the median is:

Based on the empirical rule we can expect about 95 percent of the values in bell-shaped distributions to be within ± one standard deviation of the mean.

A small company has 7 employees. The numbers of years these employees have worked for this company are shown as follows: Based upon this information, the mean number of years that employees have been with this company is:

Consider a situation involving two populations where population 1 is known to have a higher coefficient of variation than population 2. In this situation, we know that population 1 has a higher standard deviation than population 2.