Deck 3: Numerical Descriptive Measures

Question 1

Which of the following is NOT sensitive to extreme values?

A) The range.
B) The standard deviation.
C) The interquartile range.
D) The coefficient of variation.

Answer 1

C

Question 2

According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______
Percent of the observations will be contained within 2 standard deviations around the arithmetic
Mean.

A) 68.26
B) 88.89
C) 93.75
D) 95.44

Answer 2

D

Question 3

According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______
Percent of the observations will be contained within 1 standard deviation around the arithmetic
Mean.

A) 68.26
B) 75.00
C) 88.89
D) 93.75

Answer 3

A

Question 4

Which measure of central tendency can be used for both numerical and categorical variables?

A) Arithmetic mean.
B) Median.
C) Mode.
D) Geometric mean.

Question 5

In a right-skewed distribution

A) the median equals the arithmetic mean.
B) the median is less than the arithmetic mean.
C) the median is greater than the arithmetic mean.
D) none of the above.

Question 6

Which of the arithmetic mean, median, mode, and geometric mean are resistant measures of
Central tendency?

A) The arithmetic mean and median only.
B) The median and mode only.
C) The mode and geometric mean only.
D) The arithmetic mean and mode only.

Question 7

When extreme values are present in a set of data, which of the following descriptive summary
Measures are most appropriate:

A) CV and range.
B) arithmetic mean and standard deviation.
C) interquartile range and median.
D) variance and interquartile range.

Question 8

Which of the following is NOT a measure of central tendency?

A) The arithmetic mean.
B) The geometric mean.
C) The mode.
D) The interquartile range.

Question 9

Which of the following statements about the median is not true?

A) It is more affected by extreme values than the arithmetic mean.
B) It is a measure of central tendency.
C) It is equal to
D) It is equal to the mode in bell-shaped "normal" distributions.

Question 10

In perfectly symmetrical distributions, which of the following is NOT a correct statement?

A) The distance from Q1 to Q2 equals to the distance from Q2 to Q3.
B) The distance from the smallest observation to Q1 is the same as the distance from Q3 to the largest observation.
C) The distance from the smallest observation to Q2 is the same as the distance from Q2 to the largest observation.
D) The distance from Q1 to Q3 is half of the distance from the smallest to the largest observation.

Question 11

In a perfectly symmetrical distribution

A) the range equals the interquartile range.
B) the interquartile range equals the arithmetic mean.
C) the median equals the arithmetic mean.
D) the variance equals the standard deviation.

Question 12

In left-skewed distributions, which of the following is the correct statement?

A) The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3.
B) The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation.
C) The distance from the smallest observation to Q2 is less than the distance from Q2 to the largest observation.
D) The distance from Q1 to Q3 is twice the distance from the Q1 to Q2.

Question 13

Which descriptive summary measures are considered to be resistant statistics?

A) The arithmetic mean and standard deviation.
B) The interquartile range and range.
C) The mode and variance.
D) The median and interquartile range.

Question 14

In general, which of the following descriptive summary measures cannot be easily approximated
From a boxplot?

A) The variance.
B) The range.
C) The interquartile range.
D) The median.

Question 15

The smaller the spread of scores around the arithmetic mean,

A) the smaller the interquartile range.
B) the smaller the standard deviation.
C) the smaller the coefficient of variation.
D) All the above.

Question 16

In right-skewed distributions, which of the following is the correct statement?

Question 17

Which of the following is sensitive to extreme values?

A) The median.
B) The interquartile range.
C) The arithmetic mean.
D) The 1st quartile.

Question 18

In a perfectly symmetrical bell-shaped "normal" distribution

A) the arithmetic mean equals the median.
B) the median equals the mode.
C) the arithmetic mean equals the mode.
D) All the above.

Question 19

Which of the following statistics is not a measure of central tendency?

A) Arithmetic mean.
B) Median.
C) Mode.
D) Q3.

Question 20

According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______
Percent of the observations will be contained within 3 standard deviations around the arithmetic
Mean.

A) 68.26
B) 75.00
C) 95.0
D) 99.7

Question 21

SCENARIO 3-1
Health care issues are receiving much attention in both academic and political arenas.A sociologist
recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for
Medicaid.The ages of 25 senior citizens were as follows:
Referring to Scenario 3-1, what type of shape does the distribution of the sample appear to have?

Question 22

True or False: The five-number summary consists of the smallest value, the first quartile, the
median, the third quartile, and the largest value.

Question 23

True or False: In left-skewed distributions, the distance from the smallest value to Q1 is greater
than the distance from Q3 to the largest value.

Question 24

True or False: A boxplot is a graphical representation of a five-number summary.

Question 25

True or False: In a set of numerical data, the value for Q3 can never be smaller than the value for
Q1.

Question 26

SCENARIO 3-1
Health care issues are receiving much attention in both academic and political arenas.A sociologist
recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for
Medicaid.The ages of 25 senior citizens were as follows:
Referring to Scenario 3-1, calculate the kurtosis statistic for the age of the senior citizens accurate
to two decimal places.

Question 27

According to the Chebyshev rule, at least what percentage of the observations in any data set are
Contained within a distance of 2 standard deviations around the mean?

A) 67%
B) 75%
C) 88.89%
D) 95%

Question 28

Which of the following is the easiest to compute?

A) The arithmetic mean.
B) The median.
C) The mode.
D) The geometric mean.

Question 29

True or False: In a set of numerical data, the value for Q2 is always halfway between Q1 and Q3.

Question 30

SCENARIO 3-1
Health care issues are receiving much attention in both academic and political arenas.A sociologist
recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for
Medicaid.The ages of 25 senior citizens were as follows:
Referring to Scenario 3-1, does the distribution of the sample appear to be lepokurtic or
platykurtic?

Question 31

SCENARIO 3-1
Health care issues are receiving much attention in both academic and political arenas.A sociologist
recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for
Medicaid.The ages of 25 senior citizens were as follows:
Referring to Scenario 3-1, determine the interquartile range of the ages of the senior citizens.

Question 32

True or False: If the distribution of a data set were perfectly symmetrical, the distance from Q1 to
the median would always equal the distance from Q3 to the median in a boxplot.

Question 33

According to the Chebyshev rule, at least 93.75% of all observations in any data set are contained
Within a distance of how many standard deviations around the mean?

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

Question 34

According to the Chebyshev rule, at least what percentage of the observations in any data set are
Contained within a distance of 3 standard deviations around the mean?

A) 67%
B) 75%
C) 88.89%
D) 99.7%

Question 35

A manufacturer of flashlight batteries took a sample of 130 batteries from a day's production and
Used them continuously until they were drained.The number of hours until failure are recorded.
Given below is the boxplot of the number of hours it took to drain each of the 130 batteries.The
Distribution of the number of hours is

Question 36

True or False: In right-skewed distributions, the distance from Q3 to the largest value is greater
than the distance from the smallest observation to Q1.

Question 37

SCENARIO 3-1
Health care issues are receiving much attention in both academic and political arenas.A sociologist
recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for
Medicaid.The ages of 25 senior citizens were as follows:
Referring to Scenario 3-1, determine which of the following is the correct statement.

A) One fourth of the senior citizens sampled are below 65.5 years of age.
B) The middle 50% of the senior citizens sampled are between 65.5 and 73.0 years of age.
C) The mean age of senior citizens sampled is 73.5 years of age.
D) All of the above are correct.

Question 38

SCENARIO 3-1
Health care issues are receiving much attention in both academic and political arenas.A sociologist
recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for
Medicaid.The ages of 25 senior citizens were as follows:
Referring to Scenario 3-1, identify which of the following is the correct statement.

A) One fourth of the senior citizens sampled are below 64 years of age.
B) The middle 50% of the senior citizens sampled are between 65.5 and 73.0 years of age.
C) 25% of the senior citizens sampled are older than 81.5 years of age.
D) All of the above are correct.

Question 39

According to the Chebyshev rule, at least 75% of all observations in any data set are contained
Within a distance of how many standard deviations around the mean?

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

Question 40

SCENARIO 3-1
Health care issues are receiving much attention in both academic and political arenas.A sociologist
recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for
Medicaid.The ages of 25 senior citizens were as follows:
Referring to Scenario 3-1, calculate the variance of the ages of the senior citizens correct to the
nearest hundredth of a year squared.

Question 41

True or False: The line drawn within the box of the boxplot always represents the median.

Question 42

True or False: In exploratory data analysis, a boxplot can be used to illustrate the median,
quartiles, and extreme values.

Question 43

True or False: The interquartile range is a measure of central tendency in a set of data.

Question 44

True or False: The coefficient of variation is a measure of relative variation.

Question 45

True or False: If the data set is approximately bell-shaped, the empirical rule will more accurately
reflect the greater concentration of data close to the mean as compared to the Chebyshev rule.

Question 46

If the arithmetic mean of a numerical data set is greater than the median, the data are considered
to be _______ skewed.

Question 47

True or False: The line drawn within the box of the boxplot always represents the arithmetic
mean.

Question 48

True or False: A population with 200 elements has an arithmetic mean of 10.From this
information, it can be shown that the population standard deviation is 15.

Question 49

True or False: In a sample of size 40, the sample mean is 15.In this case, the sum of all
observations in the sample is

Question 50

True or False: The geometric mean is useful in measuring the rate of change of a variable over
time.

Question 51

True or False: The coefficient of variation measures variability in a data set relative to the size of
the arithmetic mean.

Question 52

True or False: The geometric mean is a measure of variation or dispersion in a set of data.

Question 53

SCENARIO 3-2
The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a
sample of 11 different servings.
Referring to Scenario 3-2, the arithmetic mean carbohydrates in this sample is ________ grams.

Question 54

True or False: In a boxplot, the box portion represents the data between the first and third quartile
values.

Question 55

SCENARIO 3-2
The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a
sample of 11 different servings.
Referring to Scenario 3-2, the median carbohydrate amount in the cereal is ________ grams.

Question 56

True or False: The interquartile range is a measure of variation or dispersion in a set of data.

Question 57

True or False: The coefficient of variation is a measure of central tendency in the data.

Question 58

True or False: The coefficient of variation is expressed as a percentage.

Question 59

True or False: The median of a data set with 20 items would be the average of the 10th and the
11th items in the ordered array.

Question 60

True or False: If a set of data is perfectly symmetrical, the arithmetic mean must be identical to
the median.

Question 61

SCENARIO 3-2
The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a
sample of 11 different servings.
Referring to Scenario 3-2, the range in the carbohydrate amounts is ________ grams.

Question 62

SCENARIO 3-3
The ordered array below represents the number of vitamin supplements sold by a health food store in
a sample of 16 days. Note: For this sample, the sum of the values is 448, and the sum of the squared differences between
each value and the mean is 812.
Referring to Scenario 3-3, is the number of vitamin supplements sold in this sample lepokurtic or
platykurtic?

Question 63

SCENARIO 3-3
The ordered array below represents the number of vitamin supplements sold by a health food store in
a sample of 16 days. Note: For this sample, the sum of the values is 448, and the sum of the squared differences between
each value and the mean is 812.
Referring to Scenario 3-3, the range of the number of vitamin supplements sold in this sample is
________.

Question 64

SCENARIO 3-3
The ordered array below represents the number of vitamin supplements sold by a health food store in
a sample of 16 days. Note: For this sample, the sum of the values is 448, and the sum of the squared differences between
each value and the mean is 812.
Referring to Scenario 3-3, the kurtosis statitic of the number of vitamin supplements sold in this
sample is ________.

Question 65

SCENARIO 3-2
The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a
sample of 11 different servings.
Referring to Scenario 3-2, the kurtosis statistic for the carbohydrate amount in the cereal is
________.

Question 66

SCENARIO 3-2
The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a
sample of 11 different servings.
Referring to Scenario 3-2, the third quartile of the carbohydrate amounts is ________ grams.

Question 67

SCENARIO 3-3
The ordered array below represents the number of vitamin supplements sold by a health food store in
a sample of 16 days. Note: For this sample, the sum of the values is 448, and the sum of the squared differences between
each value and the mean is 812.
Referring to Scenario 3-3, the interquartile range of the number of vitamin supplements sold in
this sample is ________.

Question 68

SCENARIO 3-2
The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a
sample of 11 different servings.
Referring to Scenario 3-2, the interquartile range in the carbohydrate amounts is ________ grams.

Question 69

SCENARIO 3-2
The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a
sample of 11 different servings.
Referring to Scenario 3-2, construct a boxplot for the carbohydrate amounts.

Question 70

SCENARIO 3-3
The ordered array below represents the number of vitamin supplements sold by a health food store in
a sample of 16 days. Note: For this sample, the sum of the values is 448, and the sum of the squared differences between
each value and the mean is 812.
Referring to Scenario 3-3, what type of shape does the distribution of the sample appear to have?

Question 71

SCENARIO 3-3
The ordered array below represents the number of vitamin supplements sold by a health food store in
a sample of 16 days. Note: For this sample, the sum of the values is 448, and the sum of the squared differences between
each value and the mean is 812.
Referring to Scenario 3-3, is the number of vitamin supplements sold in this sample right- or left-
skewed?

Question 72

SCENARIO 3-2
The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a
sample of 11 different servings.
Referring to Scenario 3-2, the five-number summary of the carbohydrate amounts consists of
________, ________, ________, ________, ________.

Question 73

SCENARIO 3-3
The ordered array below represents the number of vitamin supplements sold by a health food store in
a sample of 16 days. Note: For this sample, the sum of the values is 448, and the sum of the squared differences between
each value and the mean is 812.
Referring to Scenario 3-3, the arithmetic mean of the number of vitamin supplements sold in this
sample is ________.

Question 74

SCENARIO 3-3
The ordered array below represents the number of vitamin supplements sold by a health food store in
a sample of 16 days. Note: For this sample, the sum of the values is 448, and the sum of the squared differences between
each value and the mean is 812.
Referring to Scenario 3-3, the five-number summary of the data in this sample consists of
________, ________, ________, ________, ________.

Question 75

SCENARIO 3-2
The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a
sample of 11 different servings.
Referring to Scenario 3-2, is the carbohydrate amount in the cereal leptokurtic or platykurtic?

Question 76

SCENARIO 3-2
The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a
sample of 11 different servings.
Referring to Scenario 3-2, is the carbohydrate amount in the cereal right- or left-skewed?

Question 77

SCENARIO 3-3
The ordered array below represents the number of vitamin supplements sold by a health food store in
a sample of 16 days. Note: For this sample, the sum of the values is 448, and the sum of the squared differences between
each value and the mean is 812.
Referring to Scenario 3-3, the third quartile of the number of vitamin supplements sold in this
sample is ________.

Question 78

SCENARIO 3-2
The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a
sample of 11 different servings.
Referring to Scenario 3-2, the first quartile of the carbohydrate amounts is ________ grams.

Question 79

SCENARIO 3-3
The ordered array below represents the number of vitamin supplements sold by a health food store in
a sample of 16 days. Note: For this sample, the sum of the values is 448, and the sum of the squared differences between
each value and the mean is 812.
Referring to Scenario 3-3, construct a boxplot for the data in this sample.

Question 80

SCENARIO 3-3
The ordered array below represents the number of vitamin supplements sold by a health food store in
a sample of 16 days. Note: For this sample, the sum of the values is 448, and the sum of the squared differences between
each value and the mean is 812.
Referring to Scenario 3-3, the first quartile of the number of vitamin supplements sold in this
sample is ________.