Deck 4: Descriptive Statistics

Question 1

It is inappropriate to apply the Empirical Rule to a population that is right-skewed.
E.R. applies to normal populations.

Answer 1

True

Question 2

In a left-skewed distribution, we expect that the median will be greater than the mean.

Answer 2

True

Question 3

The midhinge is a robust measure of center when there are outliers.

Answer 3

True

Question 4

When data are right-skewed, we expect the median to be greater than the mean.

Question 5

The second quartile is the same as the median.

Question 6

If the standard deviations of two samples are the same, so are their coefficients of variation.C.V.

Question 7

One benefit of the box plot is that it clearly displays the standard deviation.

Question 8

Chebyshev's Theorem says that at least 95 percent of the data lie within 2 standard deviations of the mean.

Question 9

A certain health maintenance organization (HMO) examined the number of office visits by its members in the last year. For this data set, the mean is probably not a very good measure of a "typical" person's office visits.

Question 10

If there are 20 data values, the median will be halfway between two data values.

Question 11

If there are 19 data values, the median will have 10 values above it and 9 below it since n is odd.

Question 12

Given the data set 2, 5, 10, 6, 3, the median value is 3.

Question 13

Given the data set 10, 5, 2, 6, 3, 4, 20, the median value is 5.

Question 14

A trimmed mean may be preferable to a mean when a data set has extreme values.

Question 15

A certain health maintenance organization (HMO) examined the number of office visits by its members in the last year. This data set would probably be skewed to the left due to low outliers.

Question 16

The sum of the deviations around the mean is always zero.

Question 17

Referring to this box plot of ice cream fat content, the median seems more "typical" of fat content than the midrange as a measure of center.

Question 18

Chebyshev's Theorem says that at most 50 percent of the data lie within 2 standard deviations of the mean.

Question 19

A data set with two values that are tied for the highest number of occurrences is called bimodal.

Question 20

The midrange is not greatly affected by outliers.

Question 21

Referring to this box plot of ice cream fat content, the skewness would be negative.

Question 22

The range as a measure of variability is very sensitive to extreme data values.

Question 23

The Empirical Rule can be applied to any distribution, unlike Chebyshev's theorem.
E.R. assumes a normal population, while Chebyshev applies to any population.

Question 24

The position of the median is:

A)n/2 in any sample.
B)n/2 if n is even.
C)n/2 if n is odd.
D)(n + 1)/2 in any sample.

Question 25

Which is a characteristic of the mean as a measure of center?

A)Deviations do not sum to zero when there are extreme values.
B)It is less reliable than the mode when the data are continuous.
C)It utilizes all the information in a sample.
D)It is usually equal to the median in business data.

Question 26

A sample consists of the following data: 7, 11, 12, 18, 20, 22, 43. Using the "three standard deviation" criterion, the last observation (X = 43) would be considered an outlier.

Question 27

Which is not a characteristic of the geometric mean as a measure of center?

A)It is similar to the mean if the data are skewed right.
B)It mitigates the effects of large data values.
C)It is useful in business data to calculate average growth rates.
D)It cannot be calculated when the data contain negative or zero values.

Question 28

A leptokurtic distribution is more sharply peaked (i.e., thinner tails) than a normal distribution.

Question 29

Referring to this box plot of ice cream fat content, the mean would exceed the median.

Question 30

A platykurtic distribution is more sharply peaked (i.e., thinner tails) than a normal distribution.

Question 31

A positive kurtosis coefficient in Excel indicates a leptokurtic condition in a distribution.

Question 32

The Empirical Rule assumes that the distribution of data follows a normal curve.
E.R. assumes a normal population.

Question 33

Kurtosis cannot be judged accurately by looking at a histogram.

Question 34

Outliers are data values that fall beyond ±2 standard deviations from the mean.

Question 35

Which is not a characteristic of the standard deviation?

A)It is always the square root of the variance.
B)It is not applicable when data are continuous.
C)It can be calculated when the data contain negative or zero values.
D)Its physical interpretation is not as easy as the MAD.

Question 36

In calculating the sample variance, the sum of the squared deviations around the mean is divided by n - 1 to avoid underestimating the unknown population variance.

Question 37

When applying the Empirical Rule to a distribution of grades, if a student scored one standard deviation below the mean, then she would be at the 25^th percentile of the distribution.

Question 38

Which is a characteristic of the trimmed mean as a measure of center?

A)It is similar to the mean if there are offsetting high and low extremes.
B)It is especially helpful in a small sample.
C)It does not require sorting the sample.
D)It is basically the same as the midrange.

Question 39

Referring to this graph of ice cream fat content, the second quartile is about 61.

Question 40

Which is not an advantage of the method of medians to find Q₁ and Q₃?

A)Ease of interpolating quartile positions
B)Ease of application in small data sets
C)Intuitive definitions without complex formulas
D)Same method as Excel's =QUARTILE.EXC function.

Question 41

Which is not true of an outlier?

A)It is likely to be from a different population.
B)It suggests an error in recording the data.
C)It is best discarded to get a better mean.
D)It is an anomaly that may tell the researcher something.

Question 42

Exam scores in a small class were 10, 10, 20, 20, 40, 60, 80, 80, 90, 100, 100. For this data set, which statement is incorrect concerning measures of center?

A)The median is 60.00.
B)The mode is not helpful.
C)The 5 percent trimmed mean would be awkward.
D)The geometric mean is 35.05.

Question 43

Exam scores in a small class were 0, 50, 50, 70, 70, 80, 90, 90, 100, 100. For this data set, which statement is incorrect concerning measures of center?

A)The median is 70.
B)The mode is not helpful.
C)The geometric mean is useless.
D)The mean is 70.

Question 44

Chebyshev's Theorem:

A)applies to all samples.
B)applies only to samples from a normal population.
C)gives a narrower range of predictions than the Empirical Rule.
D)is based on Sturges' Rule for data classification.The strength of Chebyshev's Theorem is that it makes no assumption about normality, while the

Question 45

Which is true of the kurtosis of a distribution?

A)A distribution that is flatter than a normal distribution (i.e., thicker tails) is mesokurtic.
B)A distribution that is more peaked than a normal distribution (i.e., thinner tails) is platykurtic.
C)It is risky to assess kurtosis if the sample size is less than 50.
D)The expected range of the kurtosis coefficient increases as n increases.

Question 46

Which is a correct statement concerning the median?

A)In a left-skewed distribution, we expect that the median will exceed the mean.
B)The sum of the deviations around the median is zero.
C)The median is an observed data value in any data set.
D)The median is halfway between Q₁ and Q₃ on a box plot.

Question 47

Estimating the mean from grouped data will tend to be most accurate when:

A)observations are distributed uniformly within classes.
B)there are few classes with wide class limits.
C)the sample is not very large and bins are wide.
D)the standard deviation is large relative to the mean.

Question 48

A population consists of the following data: 7, 11, 12, 18, 20, 22, 25. The population variance is:

A)6.07.
B)36.82.
C)5.16.
D)22.86.

Question 49

John scored 35 on Prof. Johnson's exam (Q₁ = 70 and Q₃ = 80). Based on the fences, which is correct?

A)John is unusual but not an outlier.
B)John is an outlier.
C)John is neither unusual nor an outlier.
D)John is in the 30^th percentile.

Question 50

Which of the following is not a valid description of an outlier?

A)A data value beyond the outer fences
B)A data value that is very unusual
C)A data value that lies below Q₁ or above Q₃
D)A data value several standard deviations from the mean.

Question 51

John scored 85 on Prof. Hardtack's exam (Q₁ = 40 and Q₃ = 60). Based on the fences, which is correct?

A)John is an extreme outlier.
B)John is an outlier.
C)John is not an outlier.
D)John is in the 85^th percentile.

Question 52

Which is true of skewness?

A)In business data, positive skewness is unusual.
B)In a negatively skewed distribution, the mean is likely to exceed the median.
C)Skewness often is evidenced by one or more outliers.
D)The expected range of Excel's skewness coefficient increases as n increases.

Question 53

In a sample of 10,000 observations from a normal population, how many would you expect to lie beyond three standard deviations of the mean?

A)None of them
B)About 27
C)About 100
D)About 127

Question 54

The Excel formula for the standard deviation of a sample array named Data is:

A)=STDEV.S(Data).
B)=STANDEV(Data).
C)=STDEV.P(Data).
D)=SUM(Data)/(COUNT(Data)-1).

Question 55

Which is not true of the Empirical Rule?

A)It applies to any distribution.
B)It can be applied to fewer distributions than Chebyshev's Theorem.
C)It assumes that the distribution of data follows a bell-shaped, normal curve.
D)It predicts more observations within μ ± kσ than Chebyshev's Theorem.The

Question 56

Exam scores in a random sample of students were 0, 50, 50, 70, 70, 80, 90, 90, 90, 100. Which statement is incorrect?

A)The standard deviation is 29.61.
B)The data are slightly left-skewed.
C)The midrange and mean are almost the same.
D)The third quartile is 90.

Question 57

Consider the following data: 6, 7, 17, 51, 3, 17, 23, and 69. The range and the median are:

A)69 and 17.5.
B)66 and 17.5.
C)66 and 17.
D)69 and 17.

Question 58

For U.S. adult males, the mean height is 178 cm with a standard deviation of 8 cm and the mean weight is 84 kg with a standard deviation of 8 kg. Elmer is 170 cm tall and weighs 70 kg. It is most nearly correct to say that:

A)Elmer's weight is more unusual than his height.
B)Elmer is heavier than he is tall.
C)Height and weight have the same degree of variation.
D)Height has more variation than weight.

Question 59

Which statement is true?

A)With nominal data we can find the mode.
B)Outliers distort the mean but not the standard deviation.
C)Business and economic data are rarely skewed to the right.
D)If we sample a normal population, the sample skewness coefficient is exactly 0.

Question 60

If samples are from a normal distribution with μ = 100 and σ = 10, we expect:

A)about 68 percent of the data within 90 to 110.
B)almost all the data within 80 to 120.
C)about 95 percent of the data within 70 to 130.
D)about half the data to exceed 75.

Question 61

VenalCo Market Research surveyed 50 individuals who recently purchased a certain CD, revealing the age distribution shown below. Which statement is least defensible?

A)The mean age probably exceeds the median age.
B)The mode would be a reasonable measure of center.
C)The data are somewhat skewed to the left.
D)The CD is unlikely to appeal to retirees.

Question 62

In the following data set {7, 5, 0, 2, 7, 15, 5, 2, 7, 18, 7, 3, 0}, the value 7 is:

A)the mean.
B)the mode.
C)both the mode and median.
D)both the mean and mode.

Question 63

Which distribution is least likely to be skewed to the right by high values?

A)Annual incomes of n passengers on a flight from New York to London
B)Weekend gambling losses of n customers at a major casino
C)Accident damage losses by n renters of an auto rental company
D)Cost of a plain McDonald's hamburger in n U.S. cities

Question 64

The ______________ shows the relationship between two variables.

A)box plot
B)bar chart
C)histogram
D)scatter plot

Question 65

If the mean and median of a population are the same, then its distribution is:

A)normal.
B)skewed.
C)symmetric.
D)uniform.

Question 66

When a sample has an odd number of observations, the median is the:

A)observation in the center of the data array.
B)average of the two observations in the center of the data array.
C)value of the most frequent observation.
D)average of Q₁ and Q₃.

Question 67

As a measure of variability, compared to the range, an advantage of the standard deviation is:

A)being calculated easily through the use of a formula.
B)considering only the data values in the middle of the data array.
C)describing the distance between the highest and lowest values.
D)considering all data values.

Question 68

Which statement is false?

A)The coefficient of variation cannot be used when the mean is zero.
B)The standard deviation is in the same units as the mean (e.g., kilograms).
C)The mean from a frequency tabulation may differ from the mean from raw data.
D)The skewness coefficient is zero in a sample from any normal distribution.

Question 69

Which Excel function would be least useful to calculate the quartiles for a column of data?

A)=STANDARDIZE
B)=PERCENTILE.EXC
C)=QUARTILE.EXC
D)=RANK

Question 70

The 25^th percentile for waiting time in a doctor's office is 19 minutes. The 75^th percentile is 31 minutes. Which is incorrect regarding the fences?

A)The upper inner fence is 49 minutes.
B)The upper outer fence is 67 minutes.
C)A waiting time of 45 minutes exceeds the upper inner fence.
D)A waiting time of 70 minutes would be an outlier.

Question 71

Frieda is 67 inches tall and weighs 135 pounds. Women her age have a mean height of 65 inches with a standard deviation of 2.5 inches and a mean weight of 125 pounds with a standard deviation of 10 pounds. In relative terms, it is correct to say that:

A)Frieda is taller and thinner than women in her age group.
B)for this group of women, weight has greater variation than height.
C)Frieda's height is more unusual than her weight.
D)the variation coefficient exceeds 10 percent for both height and weight.

Question 72

A sample of customers from Barnsboro National Bank shows an average account balance of $315 with a standard deviation of $87. A sample of customers from Wellington Savings and Loan shows an average account balance of $8350 with a standard deviation of $1800. Which statement about account balances is correct?

A)Barnsboro Bank has more variation.
B)Wellington S&L has more variation.
C)Both have the same variation. $\overline { X ^ { * } }$ $\overline { X ^ { * } }$

Question 73

When using Chebyshev's Theorem, the minimum percentage of sample observations that will fall within two standard deviations of the mean will be __________ the percentage within two standard deviations if a normal distribution is assumed (Empirical Rule).

A)smaller than
B)greater than
C)the same as

Question 74

Given a sample of three items (X = 4, 6, 5), which statement is incorrect?

A)The geometric mean is 5.2.
B)The standard deviation is 1.
C)The coefficient of variation is 20 percent.
D)The quartiles are useless.

Question 75

Which two statistics offer robust measures of center when outliers are present?

A)Mean and mode.
B)Median and trimmed mean.
C)Midrange and geometric mean.
D)Variance and standard deviation.

Question 76

Histograms are best used to:

A)provide a visual estimate of the standard deviation.
B)show the quartiles of the data set.
C)assess the shape of the distribution.
D)reveal the interquartile range of the data set.

Question 77

A sample of 50 breakfast customers of McDonald's showed the spending below. Which statement is least likely to be correct?

A)The median is very close to the midhinge.
B)The median purchase is slightly less than $5.
C)About 75 percent of the customers spend less than $7.
D)The mean is a reasonable measure of center.

Question 78

The 25^th percentile for waiting time in a doctor's office is 19 minutes. The 75^th percentile is 31 minutes. The interquartile range is:

A)12 minutes.
B)16 minutes.
C)22 minutes.
D)impossible to determine without knowing n.

Question 79

Based on daily measurements, Bob's weight has a mean of 200 pounds with a standard deviation of 16 pounds, while Mary's weight has a mean of 125 pounds with a standard deviation of 15 pounds. Who has the smaller relative variation?

A)Bob
B)Mary
C)They are the same. $\overline { X ^ { * } }$ $\overline { X ^ { * } }$

Question 80

Which Excel function is designed to calculate z = (x - μ)/σ for a column of data?

A)=STANDARDIZE
B)=NORM.DIST
C)=STDEV.P
D)=AVEDEV