Deck 3: Descriptive Statistics and Analytics: Numerical Methods

Question 1

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

Answer 1

False

Question 2

The population mean is the average of the population measurements.

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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 5

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

Question 6

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

Question 7

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

Question 8

Range is a better measure of variation than standard deviation.

Question 9

The median is said to be resistant to extreme values.

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

In a symmetric population, the median equals the mode.

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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 22

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 23

A normal population has 99.73 percent of the population measurements within ________ standard deviation(s) of the mean.

A) 1
B) 2
C) 3
D) 4

Question 24

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 25

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 26

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 27

Another name for the 50th percentile is the ________.

A) mean
B) first quartile
C) median
D) mode
E) third quartile

Question 28

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 29

If the mean, median, and mode for a given population are all equal and the relative frequency curve has matching tails to the right and left, then we would describe the shape of the distribution of the population as ________.

A) bimodal
B) skewed to the right
C) symmetrical
D) skewed to the left

Question 30

As a measure of variation, the sample ________ is easy to understand and compute. It is based on the two extreme values and therefore may reflect an extreme measurement that is not entirely representative of the data set's variation.

A) range
B) standard deviation
C) variance
D) interquartile range
E) coefficient of variation

Question 31

If the mean is greater than the median, then the relative frequency curve is most likely to be ________.

A) skewed right
B) skewed left
C) symmetrical
D) bimodal

Question 32

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

A) mean
B) median
C) geometric mean
D) weighted mean

Question 33

When calculating the geometric mean, a quantity of 1 is added to the nth root of the product (1 + R₁)(1 + R₂) . . . (1 + R_n).

Question 34

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

A) range
B) mode
C) mean
D) median

Question 35

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 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

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 38

Which percentile describes the third quartile, Q3?

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

Question 39

Which percentile describes the first quartile, Q1?

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

Question 40

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

Question 41

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 42

In a statistics class, the following 10 scores were randomly selected: 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

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 44

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

A) total sample size and sum of the midpoints of each class
B) total sample size and sum of the weighted midpoints
C) sum of the frequency of each class and the sum of the midpoints of each class
D) sum of the frequency of each class and the sample midpoint

Question 45

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 46

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 47

The constant return that yields the same wealth at the end of the investment period as do the actual returns is the ________.

A) grouped mean
B) geometric mean
C) weighted mean
D) arithmetic mean

Question 48

Which of the following is 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 49

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 50

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) .56

Question 51

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

A) correlation coefficient
B) predicted value of y
C) y-intercept
D) slope

Question 52

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 53

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 54

As the coefficient of variation ________, risk ________.

A) increases; decreases
B) decreases; increases
C) increases; increases
D) remains constant; increases

Question 55

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 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 median?

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

Question 57

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 58

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 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

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 61

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 62

Using Chebyshev's theorem, approximate the minimum proportion of the data that will be within μ ± kσ for k = 1.6.

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

Question 63

In a hearing test, randomly selected 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

In a hearing test, randomly selected 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 66

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

A) .53
B) .77
C) −.77
D) −.53
E) −8.00

Question 67

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 68

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 69

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 70

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 71

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 72

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) .15
D) 1.5
E) 67

Question 73

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 74

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 75

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 76

In a hearing test, randomly selected 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 77

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 78

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 79

Using Chebyshev's Theorem, 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 80

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