Deck 3: Describing Data: Numerical Measures

Question 1

A sample of the paramedical fees charged by clinics revealed these amounts: $55, $49, $50, $45, $52 and $55. What is the median charge?

A) $47.50
B) $51.00
C) $52.00
D) $55.00
E) None of the choices are correct.

Answer 1

B

Question 2

A stockbroker placed the following order for a customer: -50 shares of Kaiser Aluminum preferred at $104 a share
-100 shares of GTE preferred at $25 1/4 a share
-20 shares of Boston Edison preferred at $9 1/8 a share
What is the weighted arithmetic mean price per share?

A) $25.25
B) $79.75
C) $103.50
D) $42.75
E) None of the choices are correct.

Answer 2

E

Question 3

During the past six months, the purchasing agent bought: What is the weighted arithmetic mean price per ton?

A) $87.25
B) $72.33
C) $68.47
D) $89.18
E) None of the choices are correct.

Answer 3

B

Question 4

The lengths of time (in minutes) several underwriters took to review applications for similar insurance coverage are: 50, 230, 52 and 57. What is the median length of time required to review an application?

A) 54.5
B) 141.0
C) 97.25
D) 109.0
E) None of the choices are correct.

Question 5

Using the information gathered for real estate prices in Regina and surrounding areas in the early 2000's, determine the mean of the selling prices at that time.

A) $188,330
B) $200,000
C) $125,000
D) $178,350
E) $195,600

Question 6

The U.S. Department of Education reported that for the past six years 23, 19, 15, 30, 27 and 25 women received doctorate degrees in computer and information sciences. What is the mean arithmetic annual number of women receiving this degree?

A) 15.1
B) 23.2
C) 37.9
D) 22.9
E) None of the choices are correct.

Question 7

A bottling company offers three kinds of delivery service - instant, same day and within five days. The profit per delivery varies according to the kind of delivery. The profit for an instant delivery is less than the other kinds because the driver has to go directly to a grocery store with a small load and return to the bottling plant. To find out what effect each type of delivery has on the profit picture, the company has made the following tabulation based on deliveries for the previous quarter. What is the weighted mean profit per delivery?

A) $72
B) $100
C) $142
D) $97
E) None of the choices are correct.

Question 8

The U.S. Department of Education reported that for the past seven years 4,033, 5,652, 6,407, 7,201, 8,719, 11,154, and 15,121 people received bachelor's degrees in computer and information sciences. What is the arithmetic mean annual number receiving this degree?

A) About 12,240
B) About 8,327
C) About 6,217
D) About 15,962
E) None of the choices are correct.

Question 9

A sample of light trucks using diesel fuel revealed the following distribution based on fuel efficiency, i.e., litres per 100 km. What is the arithmetic mean in litres per 100 km?

A) 16.9
B) 18.6
C) 17.0
D) 17.9
E) None of the choices are correct.

Question 10

The Investment Company Institute reported in its Mutual Fund Fact Book that the number of mutual funds increased from 410 in 1990 to 857 in 2000. What is the geometric mean annual percent increase in the number of funds?

A) 1.12
B) 7.65
C) 19.41
D) 48.66
E) None of the choices are correct.

Question 11

Using the information gathered for real estate prices in Regina and surrounding areas in the early 2000's, determine the median of the selling prices at that time.

A) $188,330
B) $200,000
C) $125,000
D) $175,000
E) $195,600

Question 12

The ages of newly hired, unskilled employees were grouped into the following distribution: What is the median age?

A) 28.50
B) 28.08
C) 25.08
D) 26.58
E) 20.00

Question 13

Using the information gathered for real estate prices in Regina and surrounding areas in the early 2000's, determine the standard deviation of the selling prices at that time.

A) $88,330
B) $20,000
C) $25,000
D) $78,350
E) $88,940

Question 14

A sample of the daily production of transceivers was organized into the following distribution. What is the mean daily production?

A) 106.4
B) 101.4
C) 111.4
D) 105.0
E) 20.0

Question 15

i. A value that is typical or representative of the data is referred to as a measure of central tendency.
ii. The arithmetic mean is the sum of the observations divided by the total number of observations iii. The value of the observation in the center after they have been arranged in numerical order is called the weighted mean

A) (i), (ii) and (iii) are all correct statements
B) (i) and, (ii) are correct statements but not (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and, (iii) are correct statements but not (i).
E) All statements are false

Question 16

A sample of single persons receiving social security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839 and $965. How many observations are below the median?

A) 0
B) 1
C) 2
D) 3
E) None of the choices are correct.

Question 17

Production of passenger cars in Japan increased from 3.94 million in 1990 to 6.74 million in 2000. What is the geometric mean annual percent increase?

A) 4.0
B) 1.9
C) 5.5
D) 16.6
E) 47.3

Question 18

The Federal Aviation Administration reported that passenger revenues on international flights increased from $528 million in 1977 to $5,100 million in 2000. What is the geometric mean annual percent increase in international passenger revenues?

A) 10.4
B) 27.9
C) 103.6
D) 9.96
E) None of the choices are correct.

Question 19

The net sales of a sample of small stamping plants were organized into the following percent frequency distribution. What is the mean net sales (in $millions)?

A) $7.09
B) $10.09
C) $8.59
D) $8.325
E) Mean cannot be computed

Question 20

The number of work stoppages in a highly industrialized region for selected months are: 6, 0, 10, 14, 8 and 0. What is the median number of stoppages?

A) 0
B) 6
C) 7
D) 8
E) None of the choices are correct.

Question 21

i. A parameter is a measurable characteristic of a sample.
ii. The weighted mean is the nth root of n observations.
iii. A statistic is a measurable characteristic of the population.

A) (i), (ii) and (iii) are all correct statements
B) (i) and, (ii) are correct statements but not (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and, (iii) are correct statements but not (i).
E) All statements are false

Question 22

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-see Connect for data file.) What were the median earnings for men for the years 1999-2008?

A) $43,000
B) $44,400
C) $44,500
D) $44,600
E) $44,700

Question 23

On a survey questionnaire, students were asked to indicate their class rank in college. If there were only four choices from which to choose, which measure(s) of central tendency would be appropriate to use for the data generated by that questionnaire item?

A) Mean and median
B) Mean and mode
C) Mode and median
D) Mode only
E) Median only

Question 24

Which measure of central tendency is used to determine the average annual percent increase?

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

Question 25

If there are an odd number of observations in a set of ungrouped data that have been arrayed from low to high or vice versa, where is the median located?

A) n
B) n/2
C) (n + 1)/2
D) n + 1/2
E) None of the choices are correct.

Question 26

AAA Heating and Air Conditioning completed 30 jobs last month with a mean revenue of $5,430 per job. The president wants to know the total revenue for the month.

A) Insufficient information to estimate.
B) $5,430
C) $54,330
D) $162,900
E) $169,200

Question 27

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-see Connect for data file.) What are the mean earnings for women for the years 1999-2008?

A) $27,000
B) $27,600
C) $27,900
D) $28,320
E) $28,600

Question 28

Three persons earn $8 an hour, six earn $9 an hour, and one earns $12 an hour. Find the weighted mean hourly wage.

A) $8
B) $9
C) $12
D) $6
E) $10

Question 29

A question in a market survey asks for a respondent's favourite car colour. Which measure of central tendency should be used to summarize this question?

A) Mode
B) Median
C) Mean
D) Geometric mean
E) Weighted mean

Question 30

Fifteen accounting majors had an average grade of 90 on a finance exam. Seven marketing majors averaged 85, while ten finance majors averaged 93 on the same exam. What is the weighted mean for the 32 students taking the exam?

A) 89.84
B) 89.33
C) 89.48
D) Impossible to determine without more information
E) None of the choices are correct.

Question 31

The number of students at a local university increased from 2,500 students 5000 students in 10 years. Based on a geometric mean, the university grew at an average percentage rate of

A) 2,500 students per year
B) 1.071 students per year
C) 7.1 percent per year
D) 250 students per year
E) Cannot be determined

Question 32

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-see Connect for data file.) What were the modal earnings for women for the years 1999-2008?

A) $27,000
B) $27,600
C) $27,900
D) $28,320
E) $28,600

Question 33

The net incomes (in $millions) of a sample of steel fabricators are: $86, $67, $86 and $85. What is the modal net income?

A) $67
B) $85
C) $85.5
D) $86
E) None of the choices are correct.

Question 34

Which one of the following is referred to as the population mean?

A) Statistic
B) µ
C) Sample
D) ∑
E) None of the choices are correct.

Question 35

For which measure of central tendency will the sum of the deviations of each value from that average always be zero?

A) Mode
B) Mean
C) Median
D) Geometric mean
E) None of the choices are correct.

Question 36

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-see Connect for data file.) What were the modal earnings for men for the years 1999-2008?

A) $43,000
B) $44,400
C) $44,500
D) $44,600
E) $44,700

Question 37

What is the median of 26, 30, 24, 32, 32, 31, 27 and 29?

A) 32
B) 29
C) 30
D) 29.5
E) None of the choices are correct.

Question 38

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-see Connect for data file.) What were the mean earnings for men for the years 1999-2008?

A) $43,000
B) $44,400
C) $44,500
D) $44,600
E) $44,700

Question 39

Which measure of central tendency is found by arranging the data from low to high, and selecting the middle value?

A) Arithmetic mean
B) Median
C) Mode
D) Geometric mean
E) None of the choices are correct.

Question 40

Listed below is the average earnings ratio by sex for full-year, full-time workers from 1999 to 2008. (Source: Adapted from Statistics Canada-see Connect for data file.) What are the median earnings for women for the years 1999-2008?

A) $27,000
B) $27,600
C) $27,900
D) $28,320
E) $28,600

Question 41

A disadvantage of using an arithmetic mean to summarize a set of data is

A) It can be used for interval and ratio data.
B) It is always different from the median.
C) It can be biased by one or two extremely small or large values.
D) The arithmetic mean sometimes has two values.

Question 42

i. For salaries of $102,000, $98,000, $45,000, $106,000 and $101,000, the arithmetic mean would be an appropriate average.
ii. Extremely high or low scores do not affect the value of the median.
Iii) Three persons earn $8 an hour, six earn $9 an hour, and one earns $12 an hour. The weighted mean hourly wage is $9.

A) (i), (ii) and (iii) are all correct statements
B) (i) and, (ii) are correct statements but not (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and, (iii) are correct statements but not (i).
E) All statements are false

Question 43

What are half of the observations always greater than?

A) Median
B) Mode
C) Mean
D) Geometric mean
E) None of the choices are correct.

Question 44

In the calculation of the arithmetic mean for grouped data, which value is used to represent all the values in a particular class?

A) The upper limit of the class
B) The lower limit of the class
C) The frequency of the class
D) The cumulative frequency preceding the class
E) None of the choices are correct.

Question 45

Referring to the printout below, describe the shape of the distribution of the corresponding histogram.

A) Positively skewed
B) Negatively skewed
C) Perfectly symmetrical
D) Statistical

Question 46

A disadvantage of using an arithmetic mean to summarize a set of data is

A) The arithmetic mean sometimes has two values.
B) It can be used for interval and ratio data
C) It is always different from the median.
D) It can be biased by one or two extremely small or large values.
E) It doesn't always exist.

Question 47

i. If there is an even number of ungrouped values, then half of the values will be less than the median.
ii. Extremely high or low scores affect the value of the median.
iii. There are always as many values above the mean as below it.

A) (i), (ii) and (iii) are all correct statements
B) (i) and, (ii) are correct statements but not (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (i) is a correct statement, but not (ii) or (iii).
E) All statements are false

Question 48

The mean, as a measure of central location would be inappropriate for which one of the following?

A) Ages of adults at a senior citizen center
B) Incomes of lawyers
C) Number of pages in textbooks on statistics
D) Marital status of college students at a particular university

Question 49

i. If there is an even number of ungrouped values, then half of the values will be less than the median.
ii. Extremely high or low scores do not affect the value of the median.
iii. There are always as many values above the mean as below it.

A) (i), (ii) and (iii) are all correct statements
B) (i) and, (ii) are correct statements but not (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (i) is a correct statement, but not (ii) or (iii).
E) All statements are false

Question 50

What must be the least scale of measurement for the median?

A) Nominal
B) Ordinal
C) Interval
D) Ratio
E) None of the choices are correct.

Question 51

Which measures of central tendency are not affected by extremely low or extremely high values?

A) Mean and median
B) Mean and mode
C) Mode and median
D) Geometric mean and mean
E) None of the choices are correct.

Question 52

Referring to the histogram below, choose the best term to describe its shape.

A) Positively skewed
B) Negatively skewed
C) Perfectly symmetrical
D) Statistical

Question 53

If a frequency distribution has open-ended intervals at the extremes, which measure of central tendency is the most difficult to estimate?

A) Median
B) Mode
C) Mean
D) All of the choices are correct.
E) None of the choices are correct.

Question 54

Sometimes, data has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be summarized as

A) symmetric
B) bimodal (having two modes)
C) positively skewed
D) negatively skewed
E) continuous

Question 55

i. For salaries of $102,000, $98,000, $45,000, $106,000 and $101,000, the arithmetic mean would be an appropriate average.
Ii) Extremely high or low scores affect the value of the median.
Iii) Three persons earn $8 an hour, six earn $9 an hour, and one earns $12 an hour. The weighted mean hourly wage is $10.

A) (i), (ii) and (iii) are all correct statements
B) (i) and, (ii) are correct statements but not (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and, (iii) are correct statements but not (i).
E) All statements are false

Question 56

The mean, as a measure of central tendency, would be inappropriate for which one of the following?

A) Ages of adults at a senior citizen center
B) Incomes of lawyers
C) Number of pages in textbooks on statistics
D) Marital status of college students at a particular university
E) None of the choices are correct.

Question 57

Which measures of central tendency always have but one value for a set of grouped or ungrouped data?

A) Mode and median
B) Mode and mean
C) Mode and geometric mean
D) Mean and median
E) None of the choices are correct.

Question 58

What is a disadvantage of the range as a measure of dispersion?

A) Based on only two observations
B) Can be distorted by a large mean
C) Not in the same units as the original data
D) Has no disadvantage

Question 59

i. For salaries of $102,000, $98,000, $45,000, $106,000 and $101,000, the median would be an appropriate average.
Ii) There are always as many values above the mean as below it.
Iii) Three persons earn $8 an hour, six earn $9 an hour, and one earns $12 an hour. The weighted mean hourly wage is $9.

A) (i), (ii) and (iii) are all correct statements
B) (i) and, (ii) are correct statements but not (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and, (iii) are correct statements but not (i).
E) All statements are false

Question 60

If a major sports star were to move into your neighbourhood, what would you expect to happen to the neighbourhood's "average" income?

A) The mean income would increase significantly
B) The median income would increase significantly
C) The modal income would increase significantly
D) The mean income would increase significantly, but the modal income and median income would decrease
E) The standard deviation of the neighbourhood's income would get smaller

Question 61

Based on the graph below, how can we best describe the shape of this distribution?

A) Relatively symmetrical
B) Positively skewed
C) Negatively skewed
D) No variation
E) Bimodal

Question 62

i. In a positively skewed distribution, the mean is always greater than the median.
ii. In a negatively skewed distribution, the mode occurs at the peak of the curve.
iii. In a negatively skewed distribution, the mode is greater than the median.

A) (i), (ii) and (iii) are all correct statements
B) (i) and, (ii) are correct statements but not (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (i) is a correct statement, but not (ii) or (iii).
E) All statements are false

Question 63

If a major sports star were to move into your neighbourhood, what would you expect to happen to the neighbourhood's "average" income?

A) The mean income would decrease significantly
B) The median income would increase significantly
C) The modal income would increase significantly
D) The mean income would increase significantly, but the median income would stay almost the same as before
E) The standard deviation of the neighbourhood's income would get smaller

Question 64

i. In a positively skewed distribution, the mean is always greater than the median.
ii. In a negatively skewed distribution, the median occurs at the peak of the curve.
iii. In a negatively skewed distribution, the mode is greater than the median.

A) (i), (ii) and (iii) are all correct statements
B) (i) and, (ii) are correct statements but not (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (i) is a correct statement, but not (ii) or (iii).
E) All statements are false

Question 65

What is the relationship among the mean, median and mode in a symmetric distribution?

A) All equal
B) Mean is always the smallest value
C) Mean is always the largest value
D) Mode is the largest value
E) None of the choices are correct.

Question 66

Which of the following measures of dispersion are based on deviations from the mean?

A) Variance
B) Standard deviation
C) Mean deviation
D) All of the choices are correct.
E) None of the choices are correct.

Question 67

i. The sum of the deviations from the mean for the set of numbers 4, 9 and 5 will equal zero.
ii. If there is an even number of ungrouped values, the median is found by arranging them from low to high and then determining the arithmetic mean of the two middle values.
Iii) For salaries of $102,000, $98,000, $45,000, $106,000 and $101,000, the arithmetic mean would be an appropriate average.

A) (i), (ii) and (iii) are all correct statements
B) (i) and, (ii) are correct statements but not (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and, (iii) are correct statements but not (i).
E) All statements are false

Question 68

What is the range for a sample of March electric bills amounts for all-electric homes of similar sizes (to the nearest dollar): $212, $191, $176, $129, $106, $92, $108, $109, $103, $121, $175 and
$194.

A) $100
B) $130
C) $120
D) $112
E) None of the choices are correct.

Question 69

Rank the measures of dispersion in terms of their relative computational difficulty from least to most difficulty.

A) Mode, median, mean
B) Range, mean deviation, variance
C) Variance, mean deviation, range
D) There is no difference

Question 70

A purchasing agent for a trucking company is shopping for replacement tires for their trucks from two suppliers. The suppliers' prices are the same. However, Supplier A's tires have an average life of 60,000 miles with a standard deviation of 10,000 miles. Supplier B's tires have an average life of
60,000 miles with a standard deviation of 2,000 miles. Which of the following statements is true?

A) The two distributions of tire life are the same
B) On average, Supplier A's tires have a longer life then Supplier B's tires
C) The life of Supplier B's tire is more predictable than the life of Supplier A's tires
D) The dispersion of Supplier A's tire life is less than the dispersion of Supplier B's tire life
E) The life of Supplier A's tire is more predictable than the life of Supplier B's tires

Question 71

The sum of the differences between sample observations and the sample mean is

A) Zero
B) The mean deviation
C) The range
D) The standard deviation
E) The mean

Question 72

Based on the graph below, how can we best describe the shape of this distribution?

A) Symmetrical
B) Positively skewed
C) Negatively skewed
D) No variation
E) Bimodal

Question 73

The ages of a sample of the typewriters used by the typists in the typing pool were organized into the following table: What is the sample variance?

A) About 10.2
B) About 6.1
C) About 14.0
D) About 3.2
E) None of the choices are correct.

Question 74

The weights (in grams) of the contents of several small bottles are 4, 2, 5, 4, 5, 2 and 6. What is the sample variance?

A) 6.92
B) 4.80
C) 1.96
D) 2.33
E) None of the choices are correct.

Question 75

Which measure of dispersion disregards the algebraic signs (plus and minus) of each difference between X and the mean?

A) Standard deviation
B) Mean deviation
C) Arithmetic mean
D) Variance
E) None of the choices are correct.

Question 76

i. In a negatively skewed distribution, the mean is always greater than the median.
ii. In a negatively skewed distribution, the median occurs at the peak of the curve.
iii. In a positively skewed distribution, the mode is greater than the median.

A) (i), (ii) and (iii) are all correct statements
B) (i) and, (ii) are correct statements but not (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (i) is a correct statement, but not (ii) or (iii).
E) All statements are false

Question 77

What is the relationship between the variance and the standard deviation?

A) Variance is the square root of the standard deviation
B) Variance is the square of the standard deviation
C) Variance is twice the standard deviation
D) No constant relationship between the variance and the standard deviation
E) None of the choices are correct.

Question 78

A population consists of all the weights of all defensive tackles on Sociable University's football team. They are: Johnson, 204 pounds; Patrick, 215 pounds; Junior, 207 pounds; Kendron, 212 pounds; Nicko, 214 pounds; and Cochran, 208 pounds. What is the population standard deviation (in pounds)?

A) About 4
B) About 16
C) About 100
D) About 40
E) None of the choices are correct.

Question 79

A survey of passengers on domestic flights revealed these distances: What is the range (in kms)?

A) 2,499
B) 1,100
C) 2,400
D) 1,999
E) None of the choices are correct.

Question 80

Based on the graph below, how can we best describe the shape of this distribution?

A) Relatively symmetrical
B) Positively skewed
C) Negatively skewed
D) No variation
E) Bimodal