Deck 4: Descriptive Statistics

Question 1

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.

Answer 1

True

Question 2

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

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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

Question 5

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

Question 6

The second quartile is the same as the median.

Question 7

The midrange is not greatly affected by outliers.

Question 8

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

Question 9

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

Question 10

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

Question 11

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 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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 21

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 22

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 23

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

Question 24

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

Question 25

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 26

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 27

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

Question 28

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 29

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

Question 30

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 31

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 32

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

Question 33

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 34

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 35

Kurtosis cannot be judged accurately by looking at a histogram.

Question 36

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 37

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

Question 38

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 39

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 40

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 41

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 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

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 44

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 45

Which is not true of an outlier?

A) It is likely to be from a different population.
B) It is suggestive of 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 46

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 47

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 48

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 49

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 50

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

Question 51

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 52

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 53

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 54

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 55

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 56

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 57

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 58

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 59

A sample of 50 breakfast customers of MacDonald'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 60

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 61

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 62

Three randomly chosen Colorado students were asked how many times they went rock climbing last month.Their replies were 5,6,7.The standard deviation is:

A) 1.212.
B) 0.816.
C) 1.000.
D) 1.056.

Question 63

Which continuous variable 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 values of x_min and x_max can be inferred accurately except in a:

A) box plot.
B) dot plot.
C) histogram.
D) scatter plot.

Question 65

Three randomly chosen California students were asked how many times they drove to Mexico last year.Their replies were 4,5,6.The geometric mean is:

A) 3.87.
B) 5.00.
C) 5.42.
D) 4.93.

Question 66

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 67

Which of the following statements is likely to be true?

A) The median personal income of California taxpayers would probably be near the mean.
B) The interquartile range offers a measure of income inequality among California residents.
C) For income,the sum of squared deviations about the mean is negative about half the time.
D) For personal incomes in California,outliers in either tail would be equally likely.

Question 68

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 69

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 70

Outliers are indicated using fences on a

A) box plot.
B) dot plot.
C) histogram.
D) Pareto chart.

Question 71

Which is not a measure of variability?

A) Mean absolute deviation (MAD)
B) Range
C) Coefficient of variation
D) Trimmed mean

Question 72

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 73

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 74

The ______________ shows the relationship between two variables.

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

Question 75

Patient survival times after a certain type of surgery have a very right-skewed distribution due to a few high outliers.Consequently,which statement is most likely to be correct?

A) Median > Midrange
B) Mean < Median
C) Mean > Midrange
D) Mean > Trimmed Mean

Question 76

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

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

Question 77

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 78

Three randomly chosen Michigan students were asked how many round trips they made to Canada last year.Their replies were 3,4,5.The geometric mean is:

A) 3.877.
B) 4.000.
C) 3.915.
D) 4.422.

Question 79

The median of 600,800,1000,1200 is:

A) 800.
B) 1000.
C) 900.

Question 80

Which statistics offer robust (resistant to outliers)measures of center?

A) Mean,midrange,mode.
B) Median,midhinge,trimmed mean.
C) Trimmed mean,midrange,midhinge.
D) Mean,mode,quartiles.