Deck 3: Numerical Descriptive Measures

Question 1

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

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

Answer 1

Mode

Question 2

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.

Answer 2

The distance from Q₁ to Q₂ is less than the distance from Q₂ to Q₃.

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 1ˢᵗ quartile

Question 5

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 6

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 7

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 8

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 9

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 10

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

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

Question 11

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 12

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 13

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 14

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 15

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 16

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 17

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 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

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 20

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 21

TABLE 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 Table 3-1 determine the first quartile of the ages of the senior citizens.

Question 22

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 23

Which of the following is the easiest to compute?

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

Question 24

TABLE 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 Table 3-1, calculate the variance of the ages of the senior citizens correct to the nearest hundredth of a year squared.

Question 25

TABLE 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 Table 3-1, determine the interquartile range of the ages of the senior citizens.

Question 26

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 27

TABLE 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 Table 3-1, what type of shape does the distribution of the sample appear to have?

Question 28

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 29

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 30

TABLE 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 Table 3-1, calculate the coefficient of variation of the ages of the senior citizens.

Question 31

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

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 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

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

Question 33

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 34

TABLE 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 Table 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 35

TABLE 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 Table 3-1, calculate the arithmetic mean age of the senior citizens to the nearest hundredth of a year.

Question 36

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

Question 37

TABLE 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 Table 3-1, determine the median age of the senior citizens.

Question 38

TABLE 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 Table 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

TABLE 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 Table 3-1 determine the third quartile of the ages of the senior citizens.

Question 40

TABLE 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 Table 3-1, calculate the standard deviation of the ages of the senior citizens correct to the nearest hundredth of a year.

Question 41

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

Question 42

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

Question 43

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

Question 44

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

Question 45

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

Question 46

The coefficient of variation is expressed as a percentage.

Question 47

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

Question 48

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 49

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

Question 50

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

Question 51

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

Question 52

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

Question 53

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

Question 54

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

Question 55

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

Question 56

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

Question 57

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 58

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

Question 59

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

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

Question 61

TABLE 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.
11 15 23 29 19 22 21 20 15 25 17
Referring to Table 3-2, construct a boxplot for the carbohydrate amounts.

Question 62

TABLE 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 Table 3-3, the arithmetic mean of the number of vitamin supplements sold in this sample is ________.

Question 63

TABLE 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.
11 15 23 29 19 22 21 20 15 25 17
Referring to Table 3-2, the coefficient of variation of the carbohydrate amounts is ________ percent.

Question 64

TABLE 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 Table 3-3, the median number of vitamin supplements sold in this sample is ________.

Question 65

TABLE 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 Table 3-3, the first quartile of the number of vitamin supplements sold in this sample is ________.

Question 66

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 67

TABLE 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.
11 15 23 29 19 22 21 20 15 25 17
Referring to Table 3-2, the median carbohydrate amount in the cereal is ________ grams.

Question 68

TABLE 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.
11 15 23 29 19 22 21 20 15 25 17
Referring to Table 3-2, the variance of the carbohydrate amounts is ________ (grams squared).

Question 69

The coefficient of variation is a measure of relative variation.

Question 70

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

Question 71

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

Question 72

TABLE 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.
11 15 23 29 19 22 21 20 15 25 17
Referring to Table 3-2, the standard deviation of the carbohydrate amounts is ________ grams.

Question 73

TABLE 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.
11 15 23 29 19 22 21 20 15 25 17
Referring to Table 3-2, the first quartile of the carbohydrate amounts is ________ grams.

Question 74

TABLE 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.
11 15 23 29 19 22 21 20 15 25 17
Referring to Table 3-2, the third quartile of the carbohydrate amounts is ________ grams.

Question 75

TABLE 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.
11 15 23 29 19 22 21 20 15 25 17
Referring to Table 3-2, the five-number summary of the carbohydrate amounts consists of ________, ________, ________, ________, ________.

Question 76

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

Question 77

TABLE 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.
11 15 23 29 19 22 21 20 15 25 17
Referring to Table 3-2, the interquartile range in the carbohydrate amounts is ________ grams.

Question 78

TABLE 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 Table 3-3, the third quartile of the number of vitamin supplements sold in this sample is ________.

Question 79

TABLE 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.
11 15 23 29 19 22 21 20 15 25 17
Referring to Table 3-2, the arithmetic mean carbohydrates in this sample is ________ grams.

Question 80

TABLE 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.
11 15 23 29 19 22 21 20 15 25 17
Referring to Table 3-2, the range in the carbohydrate amounts is ________ grams.