Deck 3: Describing Data: Numerical Measures

Question 1

A parameter is a measurable characteristic of a sample.

Answer 1

False

Question 2

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

Answer 2

True

Question 3

For an ordered data set with an even number of ungrouped values,the median is the arithmetic mean of the two middle values.

Answer 3

True

Question 4

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

Question 5

For salaries of $102,000,$98,000,$45,000,$106,000 and $101,000,the arithmetic mean would be an appropriate average.

Question 6

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

Question 7

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

Question 8

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

Question 9

The median can be determined for any set of interval-level data.

Question 10

For an ordered data set with an even number of ungrouped values,half of the values will be less than the median.

Question 11

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 12

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

Question 13

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

Question 14

A variable measured at the interval or ratio level can have more than one arithmetic mean.

Question 15

A distribution that has the same shape on either side of the center is described as symmetrical.

Question 16

In a negatively skewed distribution,the mean is greater than the median.

Question 17

A statistic is a measurable characteristic of the population.

Question 18

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

Question 19

A negatively skewed distribution is not symmetrical.The long tail is to the left or in the negative direction.

Question 20

If a variable is measured at the interval or ratio level,all the values are included when computing the mean.

Question 21

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

Question 22

In a negatively skewed distribution,the mean is smaller than the median or mode and the mode occurs at the peak of the curve.

Question 23

For a symmetrical distribution,the variance is equal to the standard deviation.

Question 24

According to the Empirical Rule,75% percent of the observations lie within plus and minus 2.00 average mean deviations.

Question 25

The mean absolute deviation is the most commonly used measure of dispersion.

Question 26

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

Question 27

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

Question 28

According to the Empirical Rule,95% percent of the observations lie within plus and minus 2.00 times (multiplied)the variance.

Question 29

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 30

Dispersion describes the degree of variation in the data.

Question 31

The mean deviation is the difference between the mean or the deviations and the arithmetic mean.

Question 32

If we find the deviation of each value from the median,the sum of these deviations is always zero.

Question 33

The Empirical Rule states that about 68% of the observation will lie within one standard deviation of the mean;about 95% of the observations will lie within two standard deviations of the mean;and virtually all (99.7%)will lie within three standard deviations of the mean.

Question 34

In a positively skewed distribution,the mode is greater than the median.

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

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 37

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 38

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 39

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

Question 40

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 41

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 42

For a data set with an odd number of observations that have been sorted or arrayed from smallest to largest values,where is the median located?

A)n
B)n/2
C)(n + 1)/2
D)n + ½

Question 43

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)$67.92

Question 44

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.

Question 45

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

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

Question 46

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

Question 47

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 location 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

Question 48

Which measure of central location is found by arranging the data from smallest to largest and selecting the middle value?

A)Arithmetic mean
B)Median
C)Mode
D)Mean
E)Standard deviation

Question 49

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)3

Question 50

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 51

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

A)µ
B)s
C) $\sigma$
D) $\chi$

Question 52

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 53

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 54

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)3.5

Question 55

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 annual arithmetic mean number of degrees awarded?

A)About 12,240
B)About 8,327
C)About 6,217
D)About 15,962

Question 56

A stockbroker placed the following order for a customer: $\bullet$ 50 shares of Kaiser Aluminum preferred at $104 a share
$\bullet$ 100 shares of GTE preferred at $25.25 a share
$\bullet$ 20 shares of Boston Edison preferred 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 57

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

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

Question 58

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

Question 59

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
E)$66.67

Question 60

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

Question 61

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
E)9.0 kg

Question 62

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 63

According to Chebyshev's Theorem,what percent of the observations lie within plus and minus 1.75 standard deviations of the mean?

A)56%
B)95%
C)67%
D)Cannot compute because it depends on the shape of the distribution

Question 64

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?

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

Question 65

A sample of the monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical distribution.The sample mean is $150 and the standard deviation is $20.Using the Empirical Rule,about 95 percent 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 66

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 67

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 above

Question 68

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 69

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

A)1
B)0
C)3 1/8
D)2 3/8

Question 70

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

Question 71

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 72

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 73

Rank the measures of dispersion in terms of their relative ease of interpretation 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 74

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

Question 75

The weights (in kilograms)of a group of crates being shipped to Panama are 95,103,110,104,105,112 and 92.What is the mean deviation?

A)5.43 kg
B)6.25 kg
C)0.53 kg
D)52.50 kg

Question 76

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

Question 77

The closing prices of a common stock have been 61.5,62,61.25,60.875 and 61.5 for the past week.What is the range?

A)$1.250
B)$1.750
C)$1.125
D)$1.875

Question 78

If the variance of the "number of daily parking tickets issued" is 100,the variance is defined as

A)"number of daily parking tickets".
B)"number of daily parking tickets" squared.
C)the absolute value of the "number of daily parking tickets".
D)the square root of the "number of daily parking tickets".

Question 79

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 80

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