Deck 3: Descriptive Statistics: Numerical Methods

Question 1

The range of the measurement is the largest measurement plus the smallest measurement.

Answer 1

False

Question 2

Chebyshev's Theorem is only of practical use when analyzing a non-mound-shaped population that is not very skewed.

Answer 2

True

Question 3

The population mean is the point estimate of the sample mean.

Answer 3

False

Question 4

The population variance is the average of the squared deviations of the individual population measurements from the population mean.

Question 5

If there are 7 classes in a frequency distribution,then the fourth class will always contain the median.

Question 6

In a symmetric population,the median equals the mode.

Question 7

The p^th percentile is a value such that (100 - p)percent of the measurements fall at or below the value.

Question 8

The mean is one component of the five-number summary.

Question 9

Data summarized in a frequency distribution or histogram form are often called weighted data.

Question 10

The weights that are used in calculating a weighted mean will vary depending on the situation.

Question 11

The population mean is the average of the population measurements.

Question 12

Range is a better measure of variation than standard deviation.

Question 13

It is appropriate to use the Empirical Rule to describe a population that is extremely skewed.

Question 14

The median is the measure of central tendency that divides a population or sample into four equal parts.

Question 15

The mode is the measurement in a sample or population that occurs most frequently.

Question 16

Z-score is often used as a measure of risk.

Question 17

The median is the value below which and above which approximately 50 percent of the measurements lie.

Question 18

A correlation coefficient close to -1 says x and y are highly related.

Question 19

The line that minimizes the sum of the squared horizontal (x)distances between the points on the scatter plot and the line is the least squares line.

Question 20

The median is said to be resistant to extreme values.

Question 21

Which percentile describes the third quartile,Q₃?

A)25^th
B)50^th
C)75^th
D)100^th

Question 22

When calculating the geometric mean,a quantity of 1 is added to the n^th root of the product (1 + R_i),where i = 1,2,...n.

Question 23

Which percentile describes the first quartile,Q₁?

A)25^th
B)50^th
C)75^th
D)100^th

Question 24

If the mean is greater than the median,then the distribution is ___________.

A)Skewed right
B)Skewed left
C)Symmetrical
D)Bimodal

Question 25

In the calculation of a mean for grouped data,we assume that the average of the measurements in each class equals the class midpoint.

Question 26

All of the following are measures of central tendency except the ____________.

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

Question 27

A disadvantage of using grouping (a frequency table)with sample data is that:

A)Calculations involving central tendency and variation are more complicated than central tendency and variation calculations based on ungrouped datA.
B)The descriptive statistics are less precise than the descriptive statistics obtained using ungrouped data.
C)The interpretation of the grouped data descriptive statistics is meaningless.
D)It is much more difficult to summarize the information than it is with the ungrouped data.

Question 28

As a measure of variation,the sample ___________ is easy to understand and compute.It is based on the two extreme values and is therefore a highly unstable measure.

A)Range
B)Standard deviation
C)Variance
D)Interquartile range
E)Coefficient of variation

Question 29

The ending value of an initial investment can be calculated using weighted means.

Question 30

Which of the following is influenced the least by the occurrence of extreme values in a sample?

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

Question 31

The average of the squared deviations of the individual population measurement from the population mean is the ___________.

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

Question 32

The measurement in a sample or a population that occurs most frequently is the ___________.

A)Mode
B)Mean
C)Median
D)Outlier
E)Average

Question 33

The geometric mean is the rate of change that yields better wealth at the end of a set of time periods than the actual returns.

Question 34

When using Chebyshev's Theorem to obtain the bounds for 99.73 percent of the values in a population,the interval generally will be ___________ the interval obtained for the same percentage if a normal distribution is assumed (Empirical Rule).

A)Shorter than
B)Wider than
C)The same as

Question 35

A normal population has 99.73 percent of the population measurements within __________ standard deviations of the mean.

A)One
B)Two
C)Three
D)Four

Question 36

A measurement located outside the upper limits of a box-and-whiskers display is ___________.

A)Always in the first quartile
B)An outlier
C)Always the largest value in the data set
D)Within the lower limits

Question 37

If a population distribution is skewed to the right,then,given a random sample from that population,one would expect that the ____________.

A)Median would be greater than the mean
B)Mode would be equal to the mean
C)Median would be less than the mean
D)Median would be equal to the mean

Question 38

A quantity that measures the variation of a population or a sample relative to its mean is called the ____________.

A)Range
B)Standard deviation
C)Coefficient of variation
D)Variance
E)Interquartile range

Question 39

Another name for the 50^th percentile is the ___________.

A)Mean
B)First quartile
C)Median
D)Mode
E)Third quartile

Question 40

If the mean,median,and mode for a given population all equal 25,then we know that the shape of the distribution of the population is ____________.

A)Bimodal
B)Skewed to the right
C)Symmetrical
D)Skewed to the left

Question 41

If b₀ = 32 and b₁ = -4 and the predicted value of y is 14,what is the value of x?

A)-24.0
B)18.0
C)4.5
D)0.56

Question 42

In a statistics class,10 scores were randomly selected with the following results were obtained: 74,73,77,77,71,68,65,77,67,66.
What is the mode?

A)71.5
B)72.0
C)77.0
D)71.0
E)73.0

Question 43

The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m. ).They selected 13 patrons and had them get in line between 2 and 3 p.m.Each was given a stopwatch to record the time they spent in line.The times recorded were as follows (in minutes).
118,124,108,116,99,120,148,118,119,121,45,130,118
What is the mean?

A)114.15
B)118
C)148
D)45
E)115.5

Question 44

In a statistics class,the following 10 scores were randomly selected: 74,73,77,77,71,68,65,77,67,66.
What is the median?

A)71.5
B)72.0
C)77.0
D)71.0
E)73.0

Question 45

A measure of the strength of the linear relationship between x and y that is dependent on the units in which x and y are measured.

A)Covariance
B)Correlation coefficient
C)Slope
D)Least squares line

Question 46

In the least squares line,___________ is defined as rise/run.

A)Correlation coefficient
B)Predicted value of y
C)Y-intercept
D)Slope

Question 47

The ______________ is a quantity that measures the variation of a population or sample relative to its mean.

A)Mean
B)Standard deviation
C)Range
D)Coefficient of variation
E)Z-score

Question 48

Quality control is an important issue at ACME Company,which manufactures light bulbs.To test the life-hours of their light bulbs,they randomly sampled nine light bulbs and measured how many hours they lasted.
378,361,350,375,200,391,375,368,321
What is the mean?

A)375
B)368
C)389.9
D)200
E)346.6

Question 49

In a hearing test,subjects estimate the loudness (in decibels)of a sound,and the results are: 68,67,70,71,68,75,68,62,80,73,68.
What is the median?

A)70
B)75
C)68
D)71
E)80

Question 50

The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m. ).They selected 13 patrons and had them get in line between 2 and 3 p.m.Each was given a stopwatch to record the time they spent in line.The times recorded were as follows (in minutes).
118,124,108,116,99,120,148,118,119,121,45,130,118
What is the median?

A)114.15
B)118
C)148
D)45
E)115.5

Question 51

In a statistics class,the following 10 scores were randomly selected: 74,73,77,77,71,68,65,77,67,66.
What is the mean?

A)71.5
B)72.0
C)77.0
D)71.0
E)73.0

Question 52

An interval that contains a specified percentage of the individual measurements is called a(n)_______________ interval.

A)Three-sigma
B)Tolerance
C)Normal
D)Empirical

Question 53

In the calculation of a mean for grouped data,___________ and ___________ are used.

A)Total sample size,sum of the midpoints of each class
B)Total sample size,sum of the weighted midpoints
C)Sum of the frequency of each class,the sum of the midpoints of each class
D)Sum of the frequency of each class,the sample midpoint

Question 54

The arithmetic mean is ___________ larger than a weighted mean in a set of data that uses unequal weights.

A)Always
B)Sometimes
C)Never

Question 55

As the coefficient of variation _______________ risk ______________.

A)Increases,Decreases
B)Decreases,Increases
C)Increases,Increases
D)Remains constant,Increases

Question 56

In a hearing test,subjects estimate the loudness (in decibels)of a sound,and the results are: 68,67,70,71,68,75,68,62,80,73,68.
What is the mean?

A)70
B)75
C)68
D)71
E)80

Question 57

The point estimate of the _______________ is the positive square root of the sample variance.

A)Sample mean
B)Sample standard deviation
C)Range
D)Median
E)Population standard deviation

Question 58

In a hearing test,subjects estimate the loudness (in decibels)of a sound,and the results are: 68,67,70,71,68,75,68,62,80,73,68.
What is the mode?

A)70
B)75
C)68
D)71
E)80

Question 59

The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m. ).They selected 13 patrons and had them get in line between 2 and 3 p.m.Each was given a stopwatch to record the time they spent in line.The times recorded were as follows (in minutes).
118,124,108,116,99,120,148,118,119,121,45,130,118
What is the mode?

A)114.15
B)118
C)148
D)45
E)115.5

Question 60

The constant return used to forecast future wealth based on actual time periods and their returns is the ____________.

A)Grouped mean
B)Geometric mean
C)Weighted mean
D)Arithmetic mean

Question 61

In a statistics class,10 scores were randomly selected with the following results (mean = 71.5):
74,73,77,77,71,68,65,77,67,66
What is the standard deviation?

A)22.72
B)12.00
C)4.77
D)516.20
E)144.00

Question 62

Using Chebyshev's Rule,find the interval that contains at least 93.75 percent of all measurements when the mean = 2.549 and s = 1.828.

A)[-2.935,8.033]
B)[-1.107,6.205]
C)[-26.699,31.797]
D)[2.435,2.663]
E)[-4.763,9.861]

Question 63

In a hearing test,subjects estimate the loudness (in decibels)of a sound,and the results are (mean = 70):
68,67,70,71,68,75,68,62,80,73,68
What is the range?

A)18
B)4.73
C)22.40
D)324
E)6.76

Question 64

Quality control is an important issue at ACME Company,which manufactures light bulbs.To test the life-hours of their light bulbs,they randomly sampled nine light bulbs and measured how many hours they lasted.
378,361,350,375,200,391,375,368,321
What is the median?

A)375
B)368
C)389.9
D)200
E)346.6

Question 65

Find the z-score for an IQ test score of 142 when the mean is 100 and the standard deviation is 15.

A)42
B)2.8
C)18.78
D)1.27
E)-2.8

Question 66

Using Chebyshev's Theorem,approximate the minimum proportion of the data that will be within µ ± kσ for k = 3.2

A)90%
B)95%
C)84%
D)97%
E)10%

Question 67

Find the z-score for an IQ test score of 92 when the mean is 100 and the standard deviation is 15.

A)0.53
B)0.77
C)-0.77
D)-0.53
E)-8.00

Question 68

Find the z-score for an IQ test score of 125 when the mean is 100 and the standard deviation is 15.

A)25
B)1.1
C)1.67
D)-1.1
E)-1.67

Question 69

Quality control is an important issue at ACME Company,which manufactures light bulbs.To test the life-hours of their light bulbs,they randomly sampled nine light bulbs and measured how many hours they lasted.
378,361,350,375,200,391,375,368,321
What is the mode?

A)375
B)368
C)389.9
D)200
E)346.6

Question 70

According to Chebyshev's Theorem,a range of how many standard deviations would include at least 80 percent of the values?

A)5.0
B)2.2
C)2.5
D)1.6
E)2.0

Question 71

In a statistics class,10 scores were randomly selected with the following results (mean = 71.5):
74,73,77,77,71,68,65,77,67,66
What is the range?

A)22.72
B)12.00
C)4.77
D)516.20
E)144.00

Question 72

According to a survey of the top 10 employers in a major city in the Midwest,a worker spends an average of 413 minutes a day on the job.Suppose the standard deviation is 26.8 minutes and the time spent is approximately a normal distribution.
What are the times within which approximately 99.73 percent of all workers will fall?

A)[305.8,520.2]
B)[386.2,439.8]
C)[372.8,453.2]
D)[359.4,466.6]
E)[332.6,493.4]

Question 73

Find the z-score for an IQ test score of 118 when the mean is 100 and the standard deviation is 15.

A)1.2
B)1.0
C)18.0
D)-1.03
E)-1.2

Question 74

In a statistics class,10 scores were randomly selected with the following results (mean = 71.5):
74,73,77,77,71,68,65,77,67,66
What is the variance?

A)22.72
B)12.00
C)4.77
D)516.20
E)144.00

Question 75

In a hearing test,subjects estimate the loudness (in decibels)of a sound,and the results are (mean = 70):
68,67,70,71,68,75,68,62,80,73,68
What is the standard deviation?

A)18
B)4.73
C)22.40
D)324
E)6.76

Question 76

According to Chebyshev's Theorem,at least what proportion of the data will be within µ ± kσ for k = 2

A)68%
B)50%
C)25%
D)75%
E)34%

Question 77

Find the coefficient of variation for IQ tests with a mean of 100 and a standard deviation of 15.

A)15.0
B)6.7
C)0.15
D)1.5
E)67

Question 78

In a hearing test,subjects estimate the loudness (in decibels)of a sound,and the results are (mean = 70):
68,67,70,71,68,75,68,62,80,73,68
What is the variance?

A)18
B)4.73
C)22.40
D)324
E)6.76

Question 79

According to a survey of the top 10 employers in a major city in the Midwest,a worker spends an average of 413 minutes a day on the job.Suppose the standard deviation is 26.8 minutes,and the time spent is approximately a normal distribution.
What are the times within which approximately 68.26 percent of all workers will fall?

A)[394.8,431.2]
B)[386.2,439.8]
C)[372.8,453.2]
D)[359.4,466.6]
E)[332.6,493.4]

Question 80

According to Chebyshev's Theorem,at least what proportion of the data will be within µ ± kσ for k = 1.6

A)39%
B)58%
C)68%
D)61%
E)92%