Deck 3: Numerically Summarizing Data

Question 1

The heights of ten male students (in inches) in a college biology class are listed below. Find the mean.71 67 67 72 76 72 73 68 72 72

A) 71 inches
B) 67 inches
C) 68 inches
D) 72 inches

Answer 1

A

Question 2

The heights of ten female students (in inches) in a college math class are listed below. Find the mean.65 66 67 66 67 70 67 70 71 68

A) 67.7 inches
B) 65.5 inches
C) 71.1 inches
D) 70.0 inches

Answer 2

A

Question 3

The repair costs for five cars which were crashed by a safety testing organization were as follows:$100, $150, $200, $250, and $150. Find the mean cost of repair.

A) $170
B) $160
C) $180
D) $140

Answer 3

A

Question 4

Which measure of central tendency may not exist for all numeric data sets?

A) Mode
B) Median
C) Mean
D) Midrange

Question 5

The median of a data set for a variable is the data value that

A) Lies in the middle of the data when the data is arranged in ascending order.
B) Appears the most often
C) Is the average, that is, the sum of all the data values of the variable divided by the number of observations in the data set?
D) None of these

Question 6

The commuting times (in minutes) of an employee for ten consecutive days are listed below. Find the mediancommute.71 67 67 72 76 72 73 68 72 72

A) 72 minutes
B) 67 minutes
C) 71 minutes
D) 73 minutes

Question 7

The following data represent a random sample of 15 complaints registered with the customer servicedepartment of a store. Determine the mode complaint.

A) other
B) defective product
C) messy store
D) no mode

Question 8

The number of students enrolled in a physics class for the last ten semesters are listed below. Find the mediannumber of students.65 66 67 66 67 70 67 70 71 68

A) 67 students
B) 66 students
C) 68 students
D) 70 students

Question 9

Each year advertisers spend billions of dollars purchasing commercial time on network sports television. In thefirst 6 months of 1988, advertisers spent $1.1 billion. A recent article listed the top 10 leading spenders (inmillions of dollars): Calculate the mean amount spent.

A) 38.81 million dollars
B) 19.52 million dollars
C) 381.01 million dollars
D) 49.40 million dollars

Question 10

If X1, X2, X3, ..., XN are the N observations of a variable from a population, then the population mean issymbolized by ~

A) μ
B) X
C) Σ
D) X

Question 11

Each year advertisers spend billions of dollars purchasing commercial time on network sports television. In thefirst 6 months of the year, advertisers spent $1.1 billion. A recent article listed the top 10 leading spenders (inmillions of dollars): Calculate the median.

A) 26.55 million dollars
B) 5.15 million dollars
C) 39.19 million dollars
D) 54.00 million dollars

Question 12

Which measure of central tendency may have more than one value in a numeric data set?

A) Mode
B) Median
C) Mean
D) Midrange

Question 13

Which measure of central tendency is not resistant to extreme values in a numeric data set?

A) Mean
B) Mode
C) Median
D) Parameters

Question 14

The commuting times of ten employees (in minutes) are listed below. Find the mode score.65 66 67 66 67 70 67 70 71 68

A) 67 minutes
B) 65 minutes
C) 66 minutes
D) 68 minutes

Question 15

The ________ of a variable is computed by determining the sum of all the values of the variable in the data setand dividing this sum by the number of observations in the data set.

A) Arithmetic mean
B) Median
C) Mode
D) Geometric mean

Question 16

The following data represents a random sample of 15 complaints registered with the customer servicedepartment of a store. Determine the median complaint.

A) No median
B) Messy store
C) Defective product
D) Excessive waiting time

Question 17

The February utility bills (in dollars) for ten residents of a large city are listed below. Find the mode amount.71 67 67 72 76 72 73 68 72 72

A) $72
B) $67
C) $76
D) $73

Question 18

A numerical summary of a population is a

A) Parameter
B) Statistic
C) Variable
D) Qualitative response

Question 19

The following data represent the bachelor degrees of CEOʹs at area small businesses. Determine the modedegree.

A) business
B) accounting
C) marketing
D) no mode

Question 20

Describe the shape of the histogram. The data set: Pick-Three lottery results for 10 consecutive weeks

A) uniform
B) symmetric
C) skewed to the left
D) skewed to the right

Question 21

Describe the shape of the histogram. The data set: age of 20 household stereo systems randomly selectedfrom a neighborhood

A) symmetric
B) uniform
C) skewed to the left
D) skewed to the right

Question 22

13, 14, 15, 16, 17

A) 4
B) 17
C) 0.8
D) 13

Question 23

Which measure of central tendency is more representative of the typical observation if the graph of the data isskewed to the right?

A) Median
B) Mean
C) Mode
D) Midrange

Question 24

Which measure of central tendency is more representative of the typical observation if the graph of the data isskewed to the left?

A) Median
B) Mean
C) Mode
D) Midrange

Question 25

Many firms use on-the-job training to teach their employees new software. Suppose you work in the personneldepartment of a firm that just finished training a group of its employees in new software, and you have beenrequested to review the performance of one of the trainees on the final test that was given to all trainees. Themean of the test scores is 76. Additional information indicated that the median of the test scores was 83. Whattype of distribution most likely describes the shape of the test scores?

A) skewed to the left
B) symmetric
C) skewed to the right
D) unable to determine with the information given

Question 26

In distributions that are skewed to the right, what is the relationship of the mean, median, and mode?

A) mean > median > mode
B) median > mean > mode
C) mode > median > mean
D) mode > mean > median

Question 27

The annual profits of five large corporations in a certain area are given below. Which measure of centraltendency should be used?$135,000 $143,000 $163,000 $133,000 $1,213,000

A) median
B) mean
C) mode
D) midrange

Question 28

3, 3, 3, 17, 29, 29, 29

A) 26
B) 16.1
C) 17
D) 169.1

Question 29

If the graph of a distribution of data shows that the graph is skewed to the right then the
D) No conclusion about the relative position of the mean and the median can be made

Question 30

Describe the shape of the histogram. The data set: round-trip commuting times (in minutes) of 20 randomlyselected employees

A) skewed to the right
B) uniform
C) skewed to the left
D) symmetric

Question 31

In distributions that are skewed to the left, what is the relationship of the mean, median, and mode?

A) mode > median > mean
B) mean > median > mode
C) mode < mean < median
D) mode > mean > median

Question 32

The output below gives the mean and median for the national dropout rates of high school students in 2010and 2012. 51Use the sample information to determine the shape of the distributions of the high school dropout rates in 2010and 2012.

Question 33

9, 20, 9, 20, 9, 20, 9, 20

A) 11
B) 20
C) 14.5
D) 22

Question 34

For the distribution drawn here, identify the mean, median, and mode.

A) A = mode, B = median, C = mean
B) A = median, B = mode, C = mean
C) A = mode, B = mean, C = median
D) A = mean, B = mode, C = median

Question 35

8, 19, 2, 13, 9

A) 17
B) 19
C) 2
D) 1

Question 36

The distribution of salaries of professional basketball players is skewed to the right. Which measure of centraltendency would be the best measure to determine the location of the center of the distribution?

A) median
B) mode
C) mean
D) frequency

Question 37

25, 34, 13, 42, 52

A) 39
B) 52
C) 13
D) 33.2

Question 38

If the graph of a distribution of data shows that the graph is skewed to the left then the
D) No conclusion about the relative position of the mean and the median can be made

Question 39

If the graph of a distribution of data shows that the graph is symmetric then the

A) Mean is a better measure of central tendency
B) Median is a better measure of central tendency
C) Mode is a better measure of central tendency
D) Midrange is a better measure of central tendency

Question 40

A severe drought affected several western states for 3 years. A Christmas tree farmer is worried about thedroughtʹs effect on the size of his trees. To decide whether the growth of the trees has been retarded, the farmerdecides to take a sample of the heights of 25 trees and obtains the following results (recorded in inches): Which measure of central tendency would be considered the best measure to use in this problem?

A) mean
B) median
C) mode
D) range

Question 41

The April precipitation amounts (in inches) for 10 cities are listed below. Find the range of the data.2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

A) 3.2 inches
B) 2.45 inches
C) 1.4 inches
D) 2.8 inches

Question 42

15, 16, 17, 18, 19

A) 1.6
B) 2.5
C) 1.3
D) 1.5

Question 43

88, 87, 21, 86, 38, 44, 43, 47, 80

A) 25.7
B) 23.0
C) 589.3
D) 530.4

Question 44

The top speeds (in mph) for a sample of five new automobile brands are listed below. Calculate the standarddeviation of the speeds.160, 125, 190, 185, 105

A) 37.2 mph
B) 28,458.00 mph
C) 153.00 mph
D) 85 mph

Question 45

11, 11, 11, 14, 17, 17, 17

A) 3
B) 2.8
C) 7.7
D) 9.0

Question 46

The book cost (in dollars) for one semesterʹs books are given below for a sample of five college students.Calculate the sample variance of the book costs.200, 130, 400, 500, 345

A) 22,450.00
B) 149.83
C) 370.00
D) 315.00

Question 47

Over the last 10 years four mutual funds all had the same mean rate of return, 12%. These mutual funds haddifferent standard deviations as follows: Mutual Money 8%, Co-joined Investments 6%, Together Fund 4%, Allfor One Fund 9%. Which mutual fund investment is the most consistent in rate of return?

A) Together Fund
B) Mutual Money
C) Co-joined Investments
D) All for One Fund

Question 48

112, 494, 230, 565, 401, 257

A) 453
B) 565
C) 112
D) 343.2

Question 49

The ages of five randomly selected students in the biology department at a private university are 30, 26, 27, 25,and 29. Calculate the sample variance of these ages.

Question 50

19, 16, 17, 12, 8, 7, 16, 9, 12

A) 4.3
B) 4.1
C) 18.6
D) 16.5

Question 51

9, 9, 7, 1, 6, 10, 9, 7, 9

A) 9
B) 10
C) 7.4
D) 11

Question 52

11, 5, 11, 13, 16, 13, 19, 12, 12, 19

A) 4.1
B) 3.8
C) 1.5
D) 3.6

Question 53

The costs (in dollars) of 10 college math textbooks are listed below. Find the sample standard deviation.70 72 71 70 69 73 69 68 70 71

A) $1.49
B) $70.30
C) $5.00
D) $2.23

Question 54

262, 296, 116, 174, 162, 287, 220, 287, 201

A) 64.3
B) 60.6
C) 4138.2
D) 3678.4

Question 55

The costs (in dollars) of 10 college math textbooks are listed below. Find the population standard deviationand the population variance.70 72 71 70 69 73 69 68 70 71

Question 56

4, 1, 8, 14, 7, 12, 16, 17, 10

A) 5.4
B) 5.1
C) 29.4
D) 26.1

Question 57

0.23, 0.12, 0.554, 0.379, 0.575, 0.257

A) 0.455
B) 0.575
C) 0.12
D) 0.353 Find the sample standard deviation.

Question 58

67, 140, 25, 90, 176

A) 151
B) 176
C) 25
D) 99.6

Question 59

The January utility bills (in dollars) for 20 residents of a large city are listed below. Find the range of the data.

A) $7
B) $2.98
C) $2
D) $1.73

Question 60

2.8, 5.8, 1.6, 4.4, 6.7, 3.8

A) 5.1
B) 6.7
C) 1.6
D) 4.2

Question 61

At a tennis tournament a statistician keeps track of every serve. The statistician reported that the mean servespeed of a particular player was 104 miles per hour (mph) and the standard deviation of the serve speeds was 8mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was bellshaped. What proportion of the playerʹs serves are expected to be between 112 mph and 120 mph?

A) 0.1350
B) 0.270
C) 0.95
D) 0.68

Question 62

A study was designed to investigate the effects of two variables - (1) a studentʹs level of mathematical anxietyand (2) teaching method - on a studentʹs achievement in a mathematics course. Students who had a low levelof mathematical anxiety were taught using the traditional expository method. These students obtained a meanscore of 460 with a standard deviation of 40 on a standardized test. Assuming a bell-shaped distribution,where would approximately 68% of the students score?

A) between 420 and 500
B) between 380 and 540
C) below 380 or above 540
D) below 420 or above 500

Question 63

True or False: Variance is the square root of standard deviation.

Question 64

The scores from a state standardized test have a bell-shaped distribution with a mean of 100 and a standarddeviation of 15. Use the Empirical Rule to find the percentage of students with scores between 70 and 130.

A) 95%
B) 68%
C) 99.7%
D) 100%

Question 65

Last year batting averages in professional baseball averaged 0.266 with a high of 0.334 and a low of 0.228(minimum 250 at-bats). Based on this information, which measure of variation could be calculated?

A) range
B) variance
C) standard deviation
D) percentile

Question 66

A small computing center has found that the number of jobs submitted per day to its computers has adistribution that is approximately bell shaped, with a mean of 84 jobs and a standard deviation of 10. Where dowe expect most (approximately 95%) of the distribution to fall?

A) between 64 and 104 jobs per day
B) between 74 and 94 jobs per day
C) between 54 and 114 jobs per day
D) between 64 and 114 jobs per day

Question 67

Health care issues are receiving much attention in both academic and political arenas. A sociologist recentlyconducted a survey of citizens over 60 years of age whose net worth is too high to qualify for governmenthealth care but who have no private health insurance. The ages of 25 uninsured senior citizens were as follows: Suppose the mean and standard deviation are 74.0 and 9.7, respectively. If we assume that the distribution ofages is bell shaped, what percentage of the respondents will be between 64.3 and 93.4 years old?

A) approximately 81.5%
B) approximately 68%
C) approximately 95%
D) approximately 83.9%

Question 68

Each year advertisers spend billions of dollars purchasing commercial time on network sports television. In thefirst 6 months of 1988, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, listedthe top 10 leading spenders (in million of dollars): Calculate the sample variance.

A) 367.36
B) 19.17
C) 38.89
D) 51.30

Question 69

A study was designed to investigate the effects of two variables - (1) a studentʹs level of mathematical anxietyand (2) teaching method - on a studentʹs achievement in a mathematics course. Students who had a low levelof mathematical anxiety were taught using the traditional expository method. These students obtained a meanscore of 460 with a standard deviation of 50 on a standardized test. Assuming a bell-shaped distribution, whatpercentage of scores exceeded 360?

A) approximately 97.5%
B) approximately 95%
C) approximately 2.5%
D) approximately 84%

Question 70

For the data set given below the sample variance will be computed. How many degrees of freedom are there?6 9 6 1 5 11 5 9 8

A) 8
B) 9
C) 1
D) 10

Question 71

The amount of television viewed by todayʹs youth is of primary concern to Parents Against WatchingTelevision (PAWT). 300 parents of elementary school-aged children were asked to estimate the number ofhours per week that their child watched television. The mean and the standard deviation for their responseswere 16 and 4, respectively. PAWT constructed a stem-and-leaf display for the data that showed that thedistribution of times was a bell-shaped distribution. Give an interval around the mean where you believe most(approximately 95%) of the television viewing times fell in the distribution.

A) between 8 and 24 hours per week
B) less than 12 and more than 20 hours per week
C) between 4 and 28 hours per week
D) between 12 and 20 hours per week

Question 72

Which is not a measure of dispersion?

A) Mean
B) Standard deviation
C) Variance
D) Range

Question 73

Many firms use on-the-job training to teach their employees new software. Suppose you work in the personneldepartment of a firm that just finished training a group of its employees in new software, and you have beenrequested to review the performance of one of the trainees on the final test that was given to all trainees. Themean and standard deviation of the test scores are 80 and 3, respectively, and the distribution of scores is bellshaped. What percentage of test-takers scored better than a trainee who scored 71?

A) approximately 99.85%
B) approximately 84%
C) approximately 95%
D) approximately 97.5%

Question 74

The _______________ is the easiest measure of dispersion to calculate.

A) Range
B) Standard deviation
C) Variance
D) Mean absolute deviation

Question 75

Solar energy is considered by many to be the energy of the future. A recent survey was taken to compare thecost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution ofthe amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $120and a standard deviation of $11. If the distribution can be considered bell shaped, what percentage of homeswill have a monthly utility bill of more than $109?

A) approximately 84%
B) approximately 95%
C) approximately 16%
D) approximately 32%

Question 76

In the computation of the sample standard variance, how many degrees of freedom are there in a data set thathas 15 data values?

A) 14
B) 15
C) 16
D) none of these

Question 77

A statistic is said to be biased if it

A) Systematically underestimates or overestimates a parameter
B) Has exactly the same value as the parameter
C) Is determined from a trimmed sample
D) Leads to an erroneous conclusion about the sample

Question 78

A severe drought affected several western states for 3 years. A Christmas tree farmer is worried about thedroughtʹs effect on the size of his trees. To decide whether the growth of the trees has been retarded, the farmerdecides to take a sample of the heights of 25 trees. Typically trees of this age have a mean height of 65 incheswith a standard deviation of 9 inches. Assuming the distribution is bell shaped, where do you expect middle95% of the tree heights to fall?

A) between 47 and 83 inches tall
B) between 56 and 74 inches tall
C) between 38 and 92 inches tall
D) over 56 inches tall

Question 79

True or False: The variance of a population is the arithmetic average of the squared deviations about thepopulation mean.

Question 80

The scores from a state standardized test have a mean of 80 and a standard deviation of 10. The distribution ofthe scores is roughly bell shaped. Use the Empirical Rule to find the percentage of scores that lie between 60and 80.

A) 47.5%
B) 68%
C) 34%
D) 95%