Deck 4: Descriptive Statistics

Question 1

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

Answer 1

True

Question 2

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

Answer 2

False

Question 3

It is inappropriate to apply the Empirical Rule to a population that is right-skewed.

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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 9

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

Question 10

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

Question 11

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

Question 12

A certain health maintenance organization 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 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

The midrange is not greatly affected by outliers.

Question 18

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 19

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

Question 20

The second quartile is the same as the median.

Question 21

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 22

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 25th percentile of the distribution.

Question 23

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

Question 24

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

Question 25

Referring to this graph of ice cream fat content,the second quartile is between 60 and 61.

Question 26

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

Question 27

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

Question 28

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 29

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

Question 30

Outliers are data values that fall beyond ±2 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

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 33

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 34

The coefficient of variation is

A)measured on a scale from 0 to 100.
B)a unit-free statistic.
C)helpful when the sample means are zero.
D)a measure of correlation for two variables.

Question 35

Kurtosis cannot be judged accurately by looking at a histogram.

Question 36

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 37

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

Question 38

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

Question 39

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 40

The Empirical Rule can be applied to any distribution,unlike Chebyshev's theorem.

Question 41

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 42

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 43

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 44

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 85th percentile.

Question 45

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 46

Which is the Excel formula for the standard deviation of a sample array named Data?

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

Question 47

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 48

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 49

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 50

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 51

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.

Question 52

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 53

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 54

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 55

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 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

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 30th percentile.

Question 58

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 59

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.

Question 60

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 61

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)=MODE

Question 62

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

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

Question 63

The 25th percentile for waiting time in a doctor's office is 19 minutes.The 75th 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 64

Shown the spending by a sample of 50 breakfast customers of McDonald's.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 65

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 66

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 67

The median of 600,800,1000,1200 is

A)800
B)1000
C)900
D)950

Question 68

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 69

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 70

The ________ shows the relationship between two variables.

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

Question 71

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 72

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

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

Question 73

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 74

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.

Question 75

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.

Question 76

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 77

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 78

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 79

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

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

Question 80

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.