Deck 3: Describing Data: Numerical Measures

Question 1

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

Answer 1

True

Question 2

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

Answer 2

True

Question 3

A set of ordinal-, interval-, or ratio-level data may only have one mode.

Answer 3

False

Question 4

The mode is the value of the observation that appears most frequently.

Question 5

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

Question 6

For any distribution, there are an equal number of values above and below the mean.

Question 7

Variation describes the degree of dispersion in the data.

Question 8

The mean deviation is the sum of the absolute differences between each value and the median.

Question 9

The sum of the deviations from the mean for the set of numbers 4, 9, and 5 will equal zero.

Question 10

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

Question 11

Extremely high or low scores affect the value of the median.

Question 12

The standard deviation is the positive square root of the variance.

Question 13

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

Question 14

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

Question 15

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.

Question 16

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

Question 17

According to Chebyshev's Theorem, 75% of the observations lie within plus and minus 2.00 average mean deviations.

Question 18

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.

Question 19

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.

Question 20

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

Question 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

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

Question 26

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

Question 27

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

A)µ
B)s
C)σ
D)χ

Question 28

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

Question 29

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

A)32
B)29
C)30
D)29.5

Question 30

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

Question 31

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.

Question 32

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 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

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

Question 34

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 + ½

Question 35

For a data set, half of the observations are always greater than the ____.

A)Median
B)Mode
C)Mean
D)Standard deviation

Question 36

What is the lowest level of measurement that a median can be computed?

A)Nominal
B)Ordinal
C)Interval
D)Ratio

Question 37

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

Question 38

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

Question 39

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

Question 40

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

Question 41

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

Question 42

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

Question 43

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.

Question 44

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

Question 45

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.

Question 46

The weights (in thousands of kilograms) of seven shipping containers are 9.5, 10.3, 11.0, 10.4, 10.5, 11.2, and 9.2. What is the mean deviation?

A)0.543 kg
B)0.625 kg
C)0.53 kg
D)5.50 kg

Question 47

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 48

The weights of a sample of crates ready for shipment to Moscow, Russia are (in kilograms): 103, 97, 101, 106, and 103. What is the mean deviation?

A)0 kg
B)6.9 kg
C)102.0 kg
D)2.4 kg

Question 49

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

A)Variance
B)Standard deviation
C)Mean deviation
D)All apply

Question 50

Ten experts rated a newly developed chocolate chip cookie on a scale of 1 to 50. Their ratings were: 34, 35, 41, 28, 26, 29, 32, 36, 38, and 40. What is the mean deviation of the ratings?

A)8.00
B)4.12
C)12.67
D)0.75

Question 51

From the least difficult to the most difficult to compute, rank the measures of dispersion.

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

Question 52

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.

Question 53

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

Question 54

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

Question 55

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%

Question 56

A sample of the personnel files of eight male employees revealed that, during a six-month period, they were absent the following number of days: 2, 0, 6, 3, 10, 4, 1, and 2. What is the mean deviation (in days)?

A)1
B)0
C)3.125
D)2.375

Question 57

What is a unique characteristic of the mean deviation?

A)It is based on only two observations.
B)It is based on deviations from the mean.
C)It uses absolute values.
D)It is only applied to skewed distributions.

Question 58

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"

Question 59

From the easiest to the hardest "ease of interpretation," rank the measures of dispersion.

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

Question 60

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

Question 61

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

Question 62

The relationship between the mean and median in a negatively skewed distribution would be that the _____________.

Question 63

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

Question 64

The measure of central location that uses all of the observations in its calculation is called the ___________.

Question 65

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

Question 66

The measure of central location that requires the data to be ranked before it is possible to determine it is called the _________.

Question 67

If a distribution is highly skewed, the measure of central location called the ________ should be avoided.

Question 68

A statistic computed by summing all of the values of a distribution and dividing by the number of values is called the __________.

Question 69

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

Question 70

A small manufacturing company with 52 employees has annual salaries distributed such that the mean is $25,459, the median is $24,798 and the mode is $24,000. An additional foreman is hired at an annual salary of $50,700. The measure of central location that is affected by the addition of this salary is called the _________________.

Question 71

In a frequency distribution, the class with the largest number of observations is called the ___________.

Question 72

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

Question 73

If a set of quantitative observations contains an extreme value, the most representative measure of central location would be the __________.

Question 74

The value that occurs most often in a set of data is called the ________.

Question 75

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%

Question 76

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%

Question 77

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

Question 78

The weekly sales from a sample of 10 computer stores yielded a mean of $25,900, a median of $25,000, and a mode of $24,500. Given this, the shape of the distribution would be _________.

Question 79

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

Question 80

The measure of central location with the smallest value in a positively skewed distribution is the _________.