# Quiz 3: Describing Data: Numerical Measures

Statistics

Q 1Q 1

A value that is typical or representative of the data is referred to as a measure of central location.

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True False

True

Q 2Q 2

The arithmetic mean is the sum of the quantitative observations divided by the total number of observations.

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True False

True

Q 3Q 3

For a set of data arranged or sorted in numerical order,the value of the observation in the center is called the weighted mean.

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True False

False

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True False

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True False

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True False

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True False

Q 8Q 8

In a sample of 10 people,3 persons earn $8 an hour,6 earn $9 an hour,and 1 earns $12 an hour. The weighted mean hourly wage is $9.

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True False

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True False

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True False

Q 11Q 11

The variance is the mean of the sum of the squared deviations between each observation and the median.

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True False

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True False

Q 13Q 13

For any data set,Chebyshev's theorem estimates the proportion of observations that occurs within k standard deviations of the mean,where k is greater than 1.0.

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True False

Q 14Q 14

In a company,the standard deviation of the ages of female employees is 6 years and the standard deviation of the ages of male employees is 10 years. These statistics indicate that the dispersion of age is greater for females than for males.

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True False

Q 15Q 15

According to the Empirical rule,about 95% of the observations lie within plus and minus 2.00 standard deviations.

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True False

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True False

Q 17Q 17

The sum of the deviations of each data value from this measure of central location will always be zero.
A)Mode
B)Mean
C)Median
D)Standard deviation

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Multiple Choice

Q 18Q 18

For any data set,which measures of central location have only one value?
A)Mode and median
B)Mode and mean
C)Mode and standard deviation
D)Mean and median

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Multiple Choice

Q 19Q 19

Which measures of central location are not affected by extremely small or extremely large values?
A)Mean and median
B)Mean and mode
C)Mode and median
D)Standard deviation and mean

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Multiple Choice

Q 20Q 20

What is the relationship among the mean,median,and mode in a symmetric distribution?
A)They are all equal.
B)The mean is always the smallest value.
C)The mean is always the largest value.
D)The mode is the largest value.

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Multiple Choice

Q 21Q 21

For a data set,half of the observations are always greater than the ________.
A)median
B)mode
C)mean
D)standard deviation

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Multiple Choice

Q 22Q 22

What is the lowest level of measurement to which a median can be computed?
A)Nominal
B)Ordinal
C)Interval
D)Ratio

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Multiple Choice

Q 23Q 23

For a data set with an odd number of observations that have been sorted from smallest to largest values,where is the median located?
A)n
B)n/2
C)(n + 1)/2
D)n + 1/2

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Multiple Choice

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Multiple Choice

Q 25Q 25

On a finance exam,15 accounting majors had an average grade of 90. On the same exam,7 marketing majors averaged 85,and 10 finance majors averaged 93. What is the weighted mean for all 32 students taking the exam?
A)89.84
B)89.33
C)89.48
D)10.67

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Multiple Choice

Q 26Q 26

A survey item asked students to indicate their class in college: freshman,sophomore,junior,or senior. Which measure(s)of central location would be appropriate for the data generated by that questionnaire item?
A)Mean and median
B)Mean and mode
C)Mode and median
D)Mode only

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Multiple Choice

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Multiple Choice

Q 28Q 28

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

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Multiple Choice

Q 29Q 29

A stockbroker placed the following order for a customer: • 50 shares of Kaiser Aluminum at $104 a share
• 100 shares of GTE at $25.25 a share
• 20 shares of Boston Edison at $9.125 a share
What is the weighted arithmetic mean price per share?
A)$25.25
B)$79.75
C)$103.50
D)$46.51

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Multiple Choice

Q 30Q 30

During the past six months,a purchasing agent placed the following three orders for coal: What is the weighted arithmetic mean price per ton?
A)$87.25
B)$72.33
C)$68.47
D)$89.18

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Multiple Choice

Q 31Q 31

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)1
B)2
C)3
D)3.5

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Multiple Choice

Q 32Q 32

Over the last six months,the following numbers of absences have been reported: 6,0,10,14,8,and 0. What is the median number of monthly absences?
A)6
B)7
C)8
D)3

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Multiple Choice

Q 33Q 33

Assume a student received the following grades for the semester: History,B; Statistics,A; Spanish,C; and English,C. History and English are 5 credit-hour courses,Statistics a 4 credit-hour course,and Spanish is a 3 credit-hour course. If 4 grade points are assigned for an A,3 for a B,and 2 for a C,what is the weighted mean grade for the semester?
A)4.00
B)1.96
C)2.76
D)3.01

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Multiple Choice

Q 34Q 34

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

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Multiple Choice

Q 35Q 35

The times (in minutes)that 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

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Multiple Choice

Q 36Q 36

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 summarized the data in the following table based on deliveries for the previous quarter. What is the weighted mean profit per delivery?
A)$72
B)$110
C)$142
D)$97

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Multiple Choice

Q 37Q 37

For the most recent seven years,the U.S. Department of Education reported the following number of bachelor's degrees awarded in computer science: 4,033; 5,652; 6,407; 7,201; 8,719; 11,154; 15,121. What is the annual arithmetic mean number of degrees awarded?
A)About 12,240
B)About 8,327
C)About 6,217
D)About 15,962

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Multiple Choice

Q 38Q 38

A question in a market survey asks for a respondent's favorite car color. Which measure of central location should be used to summarize this question?
A)Mode
B)Median
C)Mean
D)Standard deviation

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Multiple Choice

Q 39Q 39

Sometimes,a data set has two values that have the highest and equal frequencies. In this case,the distribution of the data can best be described as ________.
A)symmetric
B)bimodal (having two modes)
C)positively skewed
D)negatively skewed

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Multiple Choice

Q 40Q 40

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

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Multiple Choice

Q 41Q 41

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

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Multiple Choice

Q 42Q 42

What is a disadvantage of the range as a measure of dispersion?
A)It is based on only two observations.
B)It can be distorted by a large mean.
C)It is not in the same units as the original data.
D)It has no disadvantage.

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Multiple Choice

Q 43Q 43

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 than 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.

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Multiple Choice

Q 44Q 44

The sum of the differences between sample observations and the sample mean is equal to ________.
A)zero
B)the mean deviation
C)the range
D)the standard deviation

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Multiple Choice

Q 45Q 45

If the variance of the "number of daily parking tickets" issued is 100,the standard deviation is defined as the ________.
A)"number of daily parking tickets"
B)"number of daily parking tickets" squared
C)absolute value of the variance of the "number of daily parking tickets"
D)square root of the variance of the "number of daily parking tickets"

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Multiple Choice

Q 46Q 46

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)There is no constant relationship between the variance and the standard deviation.

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Multiple Choice

Q 47Q 47

According to Chebyshev's theorem,at least what percent of the observations lie within plus and minus 1.75 standard deviations of the mean?
A)56%
B)95%
C)67%
D)100%

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Multiple Choice

Q 48Q 48

For a sample of similar-sized all-electric homes,the March electric bills were (to the nearest dollar): $212,$191,$176,$129,$106,$92,$108,$109,$103,$121,$175,and $194. What is the range?
A)$100
B)$130
C)$120
D)$112

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Multiple Choice

Q 49Q 49

The following are the weekly amounts of welfare payments made by the federal government to a sample of six families: $139,$136,$130,$136,$147,and $136. What is the range?
A)$0
B)$14
C)$52
D)$17

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Multiple Choice

Q 50Q 50

For the past week,a company's common stock closed with the following prices: $61.5,$62,$61.25,$60.875,and $61.5. What was the price range?
A)$1.250
B)$1.750
C)$1.125
D)$1.875

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Multiple Choice

Q 51Q 51

The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical,normal distribution. The sample mean is $150 and the standard deviation is $20. Using the Empirical rule,about 95% of the monthly food expenditures are between what two amounts?
A)$100 and $200
B)$85 and $105
C)$205 and $220
D)$110 and $190

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Multiple Choice

Q 52Q 52

The ages of all the patients in the isolation ward of the hospital are 38,26,13,41,and 22. What is the population variance?
A)106.8
B)91.4
C)240.3
D)42.4

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Multiple Choice

Q 53Q 53

A sample of assistant professors on the business faculty at state-supported institutions in Ohio revealed the mean income to be $72,000 for nine months,with a standard deviation of $3,000. Using Chebyshev's theorem,what proportion of the faculty earns more than $66,000,but less than $78,000?
A)At least 50%
B)At least 25%
C)At least 75%
D)At least 100%

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Multiple Choice

Q 54Q 54

A population consists of all the weights of all defensive tackles on a 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

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Multiple Choice

Q 55Q 55

A sample of small bottles and their contents has the following weights (in grams): 4,2,5,4,5,2,and 6. What is the sample variance of bottle weight?
A)6.92
B)4.80
C)1.96
D)2.33

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Multiple Choice

Q 56Q 56

The distribution of a sample of the outside diameters of PVC pipes approximates a symmetrical,bell-shaped distribution. The arithmetic mean is 14.0 inches,and the standard deviation is 0.1 inches. About 68% of the outside diameters lie between what two amounts?
A)13.5 and 14.5 inches
B)13.0 and 15.0 inches
C)13.9 and 14.1 inches
D)13.8 and 14.2 inches

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Multiple Choice

Q 57Q 57

The sample variance of hourly wages was 10. What is the sample standard deviation?
A)$1.96
B)$4.67
C)$3.16
D)$10.00

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Multiple Choice

Q 58Q 58

Based on the Empirical rule,what percent of the observations will lie between plus or minus two standard deviations from the mean?
A)95%
B)5%
C)68%
D)2.5%

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Multiple Choice

Q 59Q 59

A sample of wires coming off the production line was tested for tensile strength. The statistical results (in PSI)were the following: According to the Empirical rule,the middle 95% of the wires tested had a tensile strength between approximately what two values?
A)450 and 550
B)460 and 540
C)420 and 580
D)380 and 620

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Multiple Choice

Q 60Q 60

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)The class midpoint

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Multiple Choice

Q 61Q 61

The net annual sales of a sample of small retail clothing stores were organized into the following relative frequency distribution. What is the mean net sales (in $ millions)?
A)$7.09
B)$10.09
C)$8.59
D)Mean cannot be computed.

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Multiple Choice

Q 62Q 62

Each person who applies for an assembly job at Robert's Electronics is given a mechanical aptitude test. One part of the test involves assembling a plug-in unit based on numbered instructions. A sample of the length of time it took 42 persons to assemble the unit was organized into the following frequency distribution. What is the standard deviation (in minutes)?
A)3.89
B)6.01
C)8.78
D)17.00

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Multiple Choice

Q 63Q 63

Consider two populations with the same mean. Since they have the same mean,then
A)their standard deviations must also be the same.
B)their medians must also be the same.
C)their modes must also be the same.
D)none of these is correct.

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Multiple Choice

Q 64Q 64

The sample mean
A)is always equal to the population mean.
B)is always smaller than the population mean.
C)is found by adding the data values and dividing them by (n − 1).
D)is found by adding all data values and dividing them by n.

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Multiple Choice

Q 65Q 65

Which measure of central location is used to determine an average annual percent increase?
A)Arithmetic mean
B)Weighted mean
C)Mode
D)Geometric mean

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Multiple Choice

Q 66Q 66

The U.S. Federal Aviation Administration reported that passenger revenues on international flights increased from $528 million in 1986 to $5,100 million in 2009. What is the geometric mean annual percent increase in international passenger revenues?
A)10.4
B)27.9
C)103.6
D)9.96

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Multiple Choice

Q 67Q 67

The Investment Research Institute reported in its Mutual Fund Fact Book that the number of mutual funds increased from 5,725 in 1999 to 7,977 in 2009. What is the geometric mean annual percent increase in the number of funds?
A)1.034
B)3.37
C)39.34
D)71.11
E)633.5

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Multiple Choice

Q 68Q 68

Production of passenger cars in Japan increased from 3.94 million in 1999 to 6.74 million in 2009. What is the geometric mean annual percent increase?
A)4.0
B)1.9
C)5.5
D)16.6
E)47.3

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Multiple Choice

Q 69Q 69

The number of students at a local university increased from 2,500 students to 5,000 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)1.072 percent per year.
C)7.2 percent per year.
D)250 students per year.

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Multiple Choice

Q 70Q 70

The variance of a sample of 121 observations equals 441. The standard deviation of the sample equals
A)11.
B)21.
C)1.91.
D)231.

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Multiple Choice

Q 71Q 71

When computing the arithmetic mean,the smallest value in the data set
A)can never be negative.
B)can never be zero.
C)can never be less than the mean.
D)can be any value.

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Multiple Choice