Deck 3: Numerical Descriptive Measures

Question 1

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

Answer 1

False

Question 2

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

Answer 2

True

Question 3

What measures variability in a data set relative to the size of the arithmetic mean?

A) Covariance
B) Coefficient of correlation
C) Central tendency
D) Coefficient of variation

Answer 3

D

Question 4

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

Question 5

What is the median of the values 3.4,4.7,1.9,and 6.5?

A) 4.125
B) 1.9
C) 8.25
D) 2.0625

Question 6

If a set of data is perfectly symmetrical,the _________must be identical to the median.

A) arithmetic mean
B) range
C) interquartile range
D) mode

Question 7

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

Question 8

An economics lecturer bases his final grade on tutorial work,two mid-semester tests,and a final examination.The tutorial work counts 10% toward the final grade,while each mid-semester test counts 25%.The remaining portion consists of the final examination.If a student scored 95% in tutorial work,70% on the first mid-semester test,96% on the second mid-semester test,and 72% on the final exam,his final average would be _________.

A) 78.9%
B) 89.7%
C) 79.8%
D) 87.9%

Question 9

In a data set with 20 items,the median would be the average of the_________ items in the ordered array.

A) 9th and 10th
B) 10th and 11th
C) 1st and 20th
D) 10th and 12th

Question 10

The coefficient of variation is a measure of relative variation.

Question 11

In right-skewed distributions,the distance from Q3 to the largest observation exceeds the distance from the smallest observation to Q1.

Question 12

What is useful in identifying extreme values or outliers?

A) The coefficient of variation
B) Z scores
C) The standard deviation
D) The sample variance

Question 13

In a sample of size 40,the sample mean is 15.What is the sum of all observations in the sample?

A) Σ X_i = 200
B) Σ X_i = 400
C) Σ X_i = 600
D) Σ X_i = 800

Question 14

In left-skewed distributions,the distance from the smallest observation to Q1 exceeds the distance from Q3 to the largest observation.

Question 15

What is a measure of variation or dispersion in a set of data?

A) The interquartile range
B) Geometric mean rate of return
C) Standard deviation
D) Coefficient of variation

Question 16

The coefficient of variation is expressed as a_________.

A) histogram
B) percentage
C) box-and-whisker plot
D) five-number summary

Question 17

As a general rule,an observation is considered an extreme value if its Z score is greater than -3.

Question 18

The larger the Z score,the further is the distance from the observation to the median.

Question 19

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

Question 20

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

Question 21

The Z score of an observation can never be negative.

Question 22

As a general rule,an observation is considered an extreme value if its Z score is less than -3.

Question 23

In a perfectly symmetrical bell-shaped "normal" distribution,the median equals the mode,the arithmetic mean equals the mode,and the arithmetic mean equals the median.

Question 24

In a right-skewed distribution the median is less than the arithmetic mean.

Question 25

The _________ of an observation measures how many standard deviations is the value from the mean.

A) Z score
B) outlier
C) coefficient of variation
D) covariance

Question 26

The more spread out,or dispersed,the data,the larger the range,interquartile range,variance and standard deviation.

Question 27

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

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

Question 28

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

A) It is equal to the mode in bell-shaped "normal" distributions.
B) It is equal to Q2.
C) It is a measure of central tendency.
D) It is more affected by extreme values than the arithmetic mean.

Question 29

As a general rule,an observation is considered an extreme value if its Z score is less than 3.

Question 30

In a perfectly symmetrical distribution

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

Question 31

The_________is a measure of how a set of data is clustered or distributed around its mean.

A) covariance
B) standard deviation
C) Z score
D) coefficient of correlation

Question 32

If the mean is greater than the median,the distribution is likely to be negative or left skewed.

Question 33

None of the measures of variation (the range,interquartile range,standard deviation and variance)can ever be negative.

Question 34

If the mean is equal to the median,the distribution is symmetrical or has zero skewness.

Question 35

The more concentrated,or homogeneous,the data,the smaller the range,interquartile range,variance and standard deviation.

Question 36

As a general rule,an observation is considered an extreme value if its Z score is greater than 3.

Question 37

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

A) Arithmetic mean and standard deviation.
B) CV and range.
C) Variance and interquartile range.
D) Interquartile range and median.

Question 38

If the mean is less than the median,the distribution is likely to be positive or right-skewed.

Question 39

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

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

Question 40

If the values are all the same (so that there is no variation in the datA.,the range,interquartile range,variance and standard deviation will all equal zero.

Question 41

Instruction 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 who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92
Referring to Instruction 3-1,identify the median age of the uninsured senior citizens.

Question 42

Instruction 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 who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92
Referring to Instruction 3-1,calculate the standard deviation of the ages of the uninsured senior citizens correct to the nearest hundredth of a year.

Question 43

Instruction 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 who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92
Referring to Instruction 3-1,identify which of the following is the correct statement.

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

Question 44

The interquartile range is not sensitive to extreme values.

Question 45

The mode is easier to compute than the geometric mean.

Question 46

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

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

Question 47

Instruction 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 who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92
Referring to Instruction 3-1,identify the third quartile of the ages of the uninsured senior citizens.

Question 48

Instruction 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 who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92
Referring to Instruction 3-1,identify the first quartile of the ages of the uninsured senior citizens.

Question 49

In right-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 Q1 to Q2 is larger than the distance from Q2 to Q3.
C) The mode is larger than the arithmetic mean.
D) The arithmetic mean is smaller than the median.

Question 50

Instruction 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 who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92
Referring to Instruction 3-1,calculate the arithmetic mean age of the uninsured senior citizens to the nearest hundredth of a year.

Question 51

Instruction 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 who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92
Referring to Instruction 3-1,what type of shape does the distribution of the sample appear to have?

Question 52

The smaller the spread of scores around the arithmetic mean,the smaller the coefficient of variation and the smaller the standard deviation.

Question 53

Certain rules can be applied when calculating the quartiles.Which of the following is NOT true about these rules.

A) If the result is a fractional half, then the quartile is equal to the mean of the corresponding ranked values.
B) If the result is an intger, then the quartile is equal to the ranked value.
C) If the result is neither an integer nor a fractional half, round the result to the nearest integer and select that ranked value.
D) None of the above.

Question 54

Instruction 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 who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92
Referring to Instruction 3-1,identify the interquartile range of the ages of the uninsured senior citizens.

Question 55

The median and interquartile range are resistant measures.

Question 56

Instruction 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 who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92
Referring to Instruction 3-1,calculate the coefficient of variation of the ages of the uninsured senior citizens.

Question 57

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

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

Question 58

Instruction 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 who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92
Referring to Instruction 3-1,identify which of the following is the correct statement.

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

Question 59

Which of the following is sensitive to extreme values?

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

Question 60

Instruction 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 who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:
60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73, 74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92
Referring to Instruction 3-1,calculate the variance of the ages of the uninsured senior citizens correct to the nearest hundredth of a year squared.

Question 61

Instruction 3-2
The data below represents 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 Instruction 3-2,the standard deviation of the carbohydrate amounts is_____________ grams.

Question 62

Instruction 3-2
The data below represents 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 Instruction 3-2,what type of shape does the distribution of the sample appear to have?

Question 63

Instruction 3-2
The data below represents 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 Instruction 3-2,the median carbohydrate amount in the cereal is _____________ grams.

Question 64

Instruction 3-3
The stem-and-leaf display below represents the number of vitamin supplements sold by a health food store in a sample of 16 days.
$$\begin{array} { | l | l | } \hline \text { Stem } & \text { Leaves } \\\hline \text { 1H } & 99 \\\hline \text { 2L } & 0023 \\\hline \text { 2H } & 567 \\\hline \text { 3L } & 034 \\\hline \text { 3H } & 568 \\\hline \text { 4L } & 1 \\\hline\end{array}$$ Note (1): 1H means the "high teens" = 15, 16, 17, 18, or 19; 2L means the "low twenties" = 20, 21, 22, 23, or 24; 2H means the "high twenties" = 25, 26, 27, 28, or 29, etc.
Note (2): For this sample, the sum of the observations is 448, the sum of the squares of the observations is 13,356, and the sum of the squared differences between each observation and the mean is 812.

-Referring to Instruction 3-3,the interquartile range of the number of vitamin supplements sold in this sample is_____________ .

Question 65

Summary measures which are not influenced by extreme values,are called _____________ .

Question 66

Instruction 3-2
The data below represents 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 Instruction 3-2,the third quartile of the carbohydrate amounts is _____________ grams.

Question 67

Instruction 3-2
The data below represents 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 Instruction 3-2,construct a box and whisker plot for the carbohydrate amounts.

Question 68

Instruction 3-2
The data below represents 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 Instruction 3-2,the variance of the carbohydrate amounts is _____________ (grams squareD..

Question 69

Instruction 3-2
The data below represents 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 Instruction 3-2,the arithmetic mean carbohydrates in this sample is _____________ grams.

Question 70

Instruction 3-3
The stem-and-leaf display below represents the number of vitamin supplements sold by a health food store in a sample of 16 days.
$$\begin{array} { | l | l | } \hline \text { Stem } & \text { Leaves } \\\hline \text { 1H } & 99 \\\hline \text { 2L } & 0023 \\\hline \text { 2H } & 567 \\\hline \text { 3L } & 034 \\\hline \text { 3H } & 568 \\\hline \text { 4L } & 1 \\\hline\end{array}$$ Note (1): 1H means the "high teens" = 15, 16, 17, 18, or 19; 2L means the "low twenties" = 20, 21, 22, 23, or 24; 2H means the "high twenties" = 25, 26, 27, 28, or 29, etc.
Note (2): For this sample, the sum of the observations is 448, the sum of the squares of the observations is 13,356, and the sum of the squared differences between each observation and the mean is 812.

-Referring to Instruction 3-3,the third quartile of the number of vitamin supplements sold in this sample is _____________ .

Question 71

Instruction 3-3
The stem-and-leaf display below represents the number of vitamin supplements sold by a health food store in a sample of 16 days.
$$\begin{array} { | l | l | } \hline \text { Stem } & \text { Leaves } \\\hline \text { 1H } & 99 \\\hline \text { 2L } & 0023 \\\hline \text { 2H } & 567 \\\hline \text { 3L } & 034 \\\hline \text { 3H } & 568 \\\hline \text { 4L } & 1 \\\hline\end{array}$$ Note (1): 1H means the "high teens" = 15, 16, 17, 18, or 19; 2L means the "low twenties" = 20, 21, 22, 23, or 24; 2H means the "high twenties" = 25, 26, 27, 28, or 29, etc.
Note (2): For this sample, the sum of the observations is 448, the sum of the squares of the observations is 13,356, and the sum of the squared differences between each observation and the mean is 812.

-Referring to Instruction 3-3,the first quartile of the number of vitamin supplements sold in this sample is _____________ .

Question 72

Instruction 3-3
The stem-and-leaf display below represents the number of vitamin supplements sold by a health food store in a sample of 16 days.
$$\begin{array} { | l | l | } \hline \text { Stem } & \text { Leaves } \\\hline \text { 1H } & 99 \\\hline \text { 2L } & 0023 \\\hline \text { 2H } & 567 \\\hline \text { 3L } & 034 \\\hline \text { 3H } & 568 \\\hline \text { 4L } & 1 \\\hline\end{array}$$ Note (1): 1H means the "high teens" = 15, 16, 17, 18, or 19; 2L means the "low twenties" = 20, 21, 22, 23, or 24; 2H means the "high twenties" = 25, 26, 27, 28, or 29, etc.
Note (2): For this sample, the sum of the observations is 448, the sum of the squares of the observations is 13,356, and the sum of the squared differences between each observation and the mean is 812.

-Referring to Instruction 3-3,the median number of vitamin supplements sold in this sample is_____________ .

Question 73

Instruction 3-2
The data below represents 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 Instruction 3-2,the range in the carbohydrate amounts is _____________ grams.

Question 74

Instruction 3-3
The stem-and-leaf display below represents the number of vitamin supplements sold by a health food store in a sample of 16 days.
$$\begin{array} { | l | l | } \hline \text { Stem } & \text { Leaves } \\\hline \text { 1H } & 99 \\\hline \text { 2L } & 0023 \\\hline \text { 2H } & 567 \\\hline \text { 3L } & 034 \\\hline \text { 3H } & 568 \\\hline \text { 4L } & 1 \\\hline\end{array}$$ Note (1): 1H means the "high teens" = 15, 16, 17, 18, or 19; 2L means the "low twenties" = 20, 21, 22, 23, or 24; 2H means the "high twenties" = 25, 26, 27, 28, or 29, etc.
Note (2): For this sample, the sum of the observations is 448, the sum of the squares of the observations is 13,356, and the sum of the squared differences between each observation and the mean is 812.

-Referring to Instruction 3-3,the arithmetic mean of the number of vitamin supplements sold in this sample is _____________ .

Question 75

Instruction 3-3
The stem-and-leaf display below represents the number of vitamin supplements sold by a health food store in a sample of 16 days.
$$\begin{array} { | l | l | } \hline \text { Stem } & \text { Leaves } \\\hline \text { 1H } & 99 \\\hline \text { 2L } & 0023 \\\hline \text { 2H } & 567 \\\hline \text { 3L } & 034 \\\hline \text { 3H } & 568 \\\hline \text { 4L } & 1 \\\hline\end{array}$$ Note (1): 1H means the "high teens" = 15, 16, 17, 18, or 19; 2L means the "low twenties" = 20, 21, 22, 23, or 24; 2H means the "high twenties" = 25, 26, 27, 28, or 29, etc.
Note (2): For this sample, the sum of the observations is 448, the sum of the squares of the observations is 13,356, and the sum of the squared differences between each observation and the mean is 812.

-Referring to Instruction 3-3,the range of the number of vitamin supplements sold in this sample is _____________ .

Question 76

Instruction 3-2
The data below represents 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 Instruction 3-2,the interquartile range in the carbohydrate amounts is _____________ grams.

Question 77

The_____________ measures the total spread of the data.

Question 78

Instruction 3-2
The data below represents 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 Instruction 3-2,the coefficient of variation of the carbohydrate amounts is _____________ percent.

Question 79

If the arithmetic mean of a numerical data set exceeds the median,the data are considered to be _____________ skewed.

Question 80

Instruction 3-2
The data below represents 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 Instruction 3-2,the first quartile of the carbohydrate amounts is _____________ grams.