Deck 3: Describing Data Using Numerical Measures

Question 1

Suppose a study of houses that have sold recently in your community showed the following frequency distribution for the number of bedrooms: Based on this information the mean number of bedrooms in houses that sold is approximately 3.26.

Answer 1

True

Question 2

The sample mean is an estimate of μ and may be either higher or lower than μ depending on the sample.

Answer 2

True

Question 3

You are given the following data: Assuming that the data reflect a sample from a larger population, the sample mean is 30.00.

Answer 3

True

Question 4

One of the primary advantages of using the median as a measure of the center for a set of data is that the median is not affected by extreme values in the data.

Question 5

A distribution is said to be symmetric when the sample mean and the population mean are equal.

Question 6

The symbol μ is used to represent the sample mean.

Question 7

You are given the following data: Assuming that the data reflect the population of interest, the mean of the population is 36.00.

Question 8

You are given the following data: Assuming that these data reflect the population of interest, these data can be considered symmetric.

Question 9

Data are considered to be right-skewed when the mean lies to the right of the median.

Question 10

A statistic is a value that describes a population characteristic while a parameter is computed from a sample.

Question 11

If after graphing the data for a quantitative variable of interest, you notice that the distribution is highly skewed in the positive direction, the measure of central location that would likely provide the best assessment of the center would be the median.

Question 12

A marketing manager for the Verizon cell phone company selected a random sample of 250 customers from the list of 10,556 total customers in a particular region. The mean monthly bill for the last six months based on the sample data is $65.70. The manager should realize that the mean bill for all 10,556 customers will actually be much higher than the sample mean of $65.70.

Question 13

A lakeside neighborhood in Washington is home to a couple of successful baseball and football players in Seattle. If news articles usually report the median household income in that neighborhood rather than the mean income, this would be because income is a left-skewed distribution.

Question 14

The Parks and Recreation manager for the city of Detroit recently submitted a report to the city council in which he indicated that a random sample of 500 park users indicated that the average number of visits per month was 4.56. This value should be viewed as a statistic by the city council.

Question 15

In a recent study of the sales prices of houses in a Midwestern city, the mean sales price has been reported to be $167,811 while the median sales price was $155,600. From this information, you can determine that the data involved in the study are left-skewed.

Question 16

Suppose a study of houses that have sold recently in your community showed the following frequency distribution for the number of bedrooms: Based on this information, the mode for the data is 140.

Question 17

You are given the following data: Assuming that these data are a sample selected from a larger population, the median value for these sample data is 25.5.

Question 18

A statistic is just another name for a parameter.

Question 19

You are given the following data: If these data were considered to be a population and you computed the mean, you would get the same answer as if these data were considered to be a sample from a larger population.

Question 20

The owner of a local gasoline station has kept track of the number of gallons of regular unleaded sold at his station every day since he purchased the station. This morning, he computed the mean number of gallons. This value would be considered a statistic.

Question 21

First Pacific Bank has determined that the mean checking account balance for all its customers is currently $743.50. Based on this, it is fair to say that about half the customers have balances exceeding $743.50.

Question 22

For a symmetric distribution, if the median value is 150 and the second quartile is 40, the fourth quartile must also be 40.

Question 23

Recently an article in a newspaper stated that 75 percent of the households in the state had incomes of $20,200 or below. Given this input, it is certain that mean household income is less than $20,200.

Question 24

When surveyed, a sample of 1,250 patients at a regional hospital provided interviewers with the following summary statistics pertaining to the hospital charges: Minimum = $278.00 Q1 = $1,245 Q2 = $3,567 Q3= $4,702. Based on these data, if you were to construct a box and whisker plot, the value corresponding to the right-hand edge of the box would be $4,702.

Question 25

The right and left edges of the box in a box and whisker plot represent the 3rd and 1st quartiles, respectively.

Question 26

A recent study involving a sample of 3,000 vehicles in California showed the following statistics related to the number of miles driven per day: Q1 = 12, Q2 = 45, and Q3 = 56. Based on these data, if a box and whisker plot is developed, a value of 110 is an outlier.

Question 27

When analyzing annual incomes of adults in a market area, the marketing manager's report indicated that the 90th percentile is $123,400. That means that 90 percent of the adult incomes in the market area fall at or below $123,400.

Question 28

In drawing a box and whisker plot the upper limit length of the whiskers is 1.5(Q3-Q1).

Question 29

The second quartile for a set of data will have the same value as the 50th percentile only when the data are symmetric.

Question 30

If a set of data has 1,500 values, the 30th percentile value will correspond to the 450th value in the data when the data have been arranged in numerical order.

Question 31

A set of data is considered to be symmetric if the 3rd quartile is three times larger than the 1st quartile.

Question 32

It is possible for a set of data to have multiple modes as well as multiple medians, but there can be only one mean.

Question 33

Suppose a study of houses that have sold recently in your community showed the following frequency distribution for the number of bedrooms: Based on this information, it is possible to determine that the distribution of bedrooms in homes sold is right-skewed.

Question 34

A box and whisker plot shows where the mean value falls relative to the median for a variable.

Question 35

If a set of data has 540 values, the 3rd quartile corresponds to approximately the 135th value when the data have been arranged in numerical order.

Question 36

Suppose a study of houses that have sold recently in your community showed the following frequency distribution for the number of bedrooms: Based on this information, the median number of bedrooms in houses sold is 3.20.

Question 37

A recent study involving a sample of 3,000 vehicles in California showed the following statistics related to the number of miles driven per day: Q1 = 12, Q2 = 45, and Q3 = 56. Based on these data, we know that the distribution is skewed.

Question 38

When the median of a data set is 110 and the mean is 127, the percentile associated with the mean must be higher than 50 percent.

Question 39

A data set in which the mean, median, and mode are all equal is said to be a skewed distribution.

Question 40

A recent study involving a sample of 3,000 vehicles in California showed the following statistics related to the number of miles driven per day: Q1 = 12, Q2 = 45, and Q3 = 56. Based on these data, if a box and whisker plot is developed, the upper limit value is 122 miles.

Question 41

A store manager tracks the number of customer complaints each week. The following data reflect a random sample of ten weeks. The variance for these data is approximately 27.78.

Question 42

The interquartile range contains the middle 50 percent of a data set.

Question 43

Populations with larger means will also have larger standard deviations since the data will be more spread out for populations with larger means.

Question 44

The interquartile range is the difference between the mean and the median.

Question 45

If a population standard deviation is computed to be 345, it will almost always be the case that a standard deviation computed from a random sample from that population will be larger than 345.

Question 46

The advantage of using the interquartile range as a measure of variation is that it utilizes all the data in its computation.

Question 47

Suppose the standard deviation for a given sample is known to be 20. If the data in the sample are doubled, the standard deviation will be significantly greater.

Question 48

The Good-Guys Car Dealership has tracked the number of used cars sold at its downtown dealership.Consider the following data as representing the population of cars sold in each of the 8 weeks that the dealership has been open. The population standard deviation is approximately 2.87 cars.

Question 49

The range is an ideal measure of variation since it is not sensitive to extreme values in the data.

Question 50

The Good-Guys Car Dealership has tracked the number of used cars sold at its downtown dealership.Consider the following data as representing the population of cars sold in each of the 8 weeks that the dealership has been open. The population variance is approximately 9.43.

Question 51

In comparing two distributions with the same mean, the coefficient of variation is the only way to assess which distribution has the greatest relative variability.

Question 52

One of the reasons that the standard deviation is preferred as a measure of variation over the variance is that the standard deviation is measured in the original units.

Question 53

For a given set of data, if the data are treated as a population, the calculated standard deviation will be less than it would be had the data been treated as a sample.

Question 54

A store manager tracks the number of customer complaints each week. The following data reflect a random sample of ten weeks. The standard deviation for these data is approximately 27.78.

Question 55

The Good-Guys Car Dealership has tracked the number of used cars sold at its downtown dealership.Consider the following data as representing the population of cars sold in each of the 8 weeks that the dealership has been open. The population range is 9.

Question 56

When a variance is calculated for a data set, the resulting value is the same regardless of whether the data set is treated as a population or a sample.

Question 57

A dairy farm in Wisconsin bottles milk in one gallon containers. At a recent meeting, the production manager asked top management for a new filling machine that he argued would assure that all containers had exactly one gallon of milk. Based on sound statistical principles, the top management group should conclude that the production manager could have merit to his argument.

Question 58

When surveyed, a sample of 1,250 patients at a regional hospital provided interviewers with the following summary statistics pertaining to the hospital charges: Minimum = $278.00 Q1 = $1,245 Q2 = $3,567 Q3= $4,702. Based on these data, if you were to construct a box and whisker plot, the value $278 would be considered an outlier.

Question 59

When surveyed, a sample of 1,250 patients at a regional hospital provided interviewers with the following summary statistics pertaining to the hospital charges: Minimum = $278.00 Q1 = $1,245 Q2 = $3,567 Q3= $4,702. Based on these data, the distribution is seen to be symmetric.

Question 60

A store manager tracks the number of customer complaints each week. The following data reflect a random sample of ten weeks. The range for these data is 8.

Question 61

The most frequently used measure of central tendency is:

A) median.
B) mean.
C) mode.
D) middle value.

Question 62

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.

Question 63

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.

Question 64

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.

Question 65

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.

Question 66

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.

Question 67

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

A) statistic.
B) parameter.
C) prime number.
D) sample value.

Question 68

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.

Question 69

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

A) 8
B) 10
C) 3
D) 12

Question 70

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.

Question 71

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.

Question 72

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.

Question 73

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

Question 74

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.

Question 75

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.

Question 76

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.

Question 77

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

A) 7.5
B) 3.5
C) 10
D) None of the above

Question 78

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.

Question 79

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

Question 80

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.