Deck 3: Numerical Descriptive Measures

Question 1

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.

Answer 1

interquartile range and median.

Question 2

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.

Answer 2

The distance from Q₁ to Q₃ is half of the distance from the smallest to the largest observation.

Question 3

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 Q₂.
D)It is equal to the mode in bell-shaped "normal" distributions.

Answer 3

It is more affected by extreme values than the arithmetic mean.

Question 4

Which of the following is sensitive to extreme values?

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

Question 5

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

A)The distance from Q₁ to Q₂ is greater than the distance from Q₂ to Q₃.
B)The distance from Q₁ to Q₂ is less than the distance from Q₂ to Q₃.
C)The arithmetic mean is less than the median.
D)The mode is greater than the arithmetic mean.

Question 6

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 7

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 8

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

Question 9

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 10

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 11

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 12

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 13

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 14

Which descriptive summary measures are 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 15

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

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

Question 16

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 17

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 18

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

Question 19

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.

Question 20

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 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 determine the third quartile of the ages of the senior citizens.

Question 22

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 median age of the senior citizens.

Question 23

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

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

Question 24

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

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

Question 25

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 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 determine the first quartile of the ages of the senior citizens.

Question 27

Data on the change in the cost of tuition,a shared dormitory room,and the most popular meal plan from one academic year to the next academic year for a sample of 100 public universities are collected.Below is the boxplot for the change in cost in dollars.The distribution of the change in cost is

A)right-skewed
B)left-skewed
C)symmetrical
D)none of the above

Question 28

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 skewness statistic for the age of the senior citizens accurate to two decimal places.

Question 29

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 arithmetic mean age of the senior citizens to the nearest hundredth of a year.

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,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 the above are correct.

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,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 the above are correct.

Question 32

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 is 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

A)right-skewed
B)left-skewed
C)symmetrical
D)none of the above

Question 33

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

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

Question 34

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 standard deviation of the ages of the senior citizens correct to the nearest hundredth of a year.

Question 35

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 36

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 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 the interquartile range of the ages of the senior citizens.

Question 38

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

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

Question 39

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 leptokurtic or platykurtic?

Question 40

Which of the following is the easiest to compute?

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

Question 41

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

Question 42

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 coefficient of variation of the ages of the senior citizens.

Question 43

The line drawn within the box of the boxplot always represents the arithmetic mean.

Question 44

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

Question 45

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 46

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 47

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

Question 48

The coefficient of variation is a measure of central tendency in the data.

Question 49

The median of the values 3.4,4.7,1.9,7.6,and 6.5 is 4.05.

Question 50

A boxplot is a graphical representation of a five-number summary.

Question 51

The median of the values 3.4,4.7,1.9,7.6,and 6.5 is 1.9.

Question 52

The line drawn within the box of the boxplot always represents the median.

Question 53

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

Question 54

In a sample of size 40,the sample mean is 15.In this case,the sum of all observations in the sample is $\Sigma$ X_i = 600.

Question 55

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

Question 56

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

Question 57

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 58

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

Question 59

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

Question 60

The coefficient of variation is expressed as a percentage.

Question 61

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

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.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
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 3-2,the standard deviation of the carbohydrate amounts is_____grams.

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.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
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 3-2,the kurtosis statistic for the carbohydrate amount in the cereal is_____.

Question 64

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 65

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.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
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 3-2,the median carbohydrate amount in the cereal is_____ grams.

Question 66

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

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.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
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 3-2,the arithmetic mean carbohydrates in this sample is_____ grams.

Question 68

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.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
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 3-2,the interquartile range in the carbohydrate amounts is_____ grams.

Question 69

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.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
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 3-2,the skewness statistic for the carbohydrate amount in the cereal is_____.

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.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
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 3-2,the range in the carbohydrate amounts is_____ grams.

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.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
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 3-2,the first quartile of the carbohydrate amounts is_____ grams.

Question 72

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

Question 73

The coefficient of variation is a measure of relative variation.

Question 74

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

Question 75

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.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
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 3-2,the variance of the carbohydrate amounts is_____ (grams squared).

Question 76

The interquartile range is a measure of central tendency in a set of data.

Question 77

If the arithmetic mean of a numerical data set is greater than the median,the data are_____skewed.

Question 78

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.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
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 3-2,is the carbohydrate amount in the cereal leptokurtic or platykurtic?

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.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
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 3-2,is the carbohydrate amount in the cereal right- or left-skewed?

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.
19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41
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 3-2,the third quartile of the carbohydrate amounts is_____ grams.