Deck 3: Numerical Descriptive Measures

Question 1

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 is 79.8%.

Answer 1

True

Question 2

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

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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

Question 5

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

Question 6

The coefficient of variation is a measure of relative variation.

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

The Z scores can be used to identify outliers.

Question 13

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 box-and-whisker plot.

Question 14

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 15

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

Question 16

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

Question 17

The coefficient of variation is expressed as a percentage.

Question 18

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

Question 19

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

Question 20

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

Question 21

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

Question 22

The Z score of an observation can never be negative.

Question 23

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

Question 24

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 25

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

Question 26

The standard deviation is a measure of how a set of data is clustered or distributed around its mean.

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

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

Question 29

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

Question 30

In a perfectly symmetrical bell-shaped "normal" distribution

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

Question 31

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

Question 32

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 33

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

Question 34

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

Question 35

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

Question 36

In a right-skewed distribution

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

Question 37

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 38

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

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

Question 41

Which descriptive summary measures are considered to be resistant statistics?

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

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:
$$\begin{array} { l l l l l l l l l l l l l } 60 & 61 & 62 & 63 & 64 & 65 & 66 & 68 & 68 & 69 & 70 & 73 & 73 \\74 & 75 & 76 & 76 & 81 & 81 & 82 & 86 & 87 & 89 & 90 & 92 &\end{array}$$

-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 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:

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

Question 44

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 45

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:

Referring to Instruction 3-1,identify the first quartile of the ages of the uninsured senior citizens.

Question 46

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:

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 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:

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:
$$\begin{array} { l l l l l l l l l l l l l } 60 & 61 & 62 & 63 & 64 & 65 & 66 & 68 & 68 & 69 & 70 & 73 & 73 \\74 & 75 & 76 & 76 & 81 & 81 & 82 & 86 & 87 & 89 & 90 & 92 &\end{array}$$

-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 49

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:

Referring to Instruction 3-1,identify the median age of the uninsured senior citizens.

Question 50

The smaller the spread of scores around the arithmetic mean

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

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:

Referring to Instruction 3-1,identify the interquartile range of the ages of the uninsured senior citizens.

Question 52

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:

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 53

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 54

Which of the following is NOT sensitive to extreme values?

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

Question 55

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:

Referring to Instruction 3-1,calculate the coefficient of variation of the ages of the uninsured senior citizens.

Question 56

Which of the following is the easiest to compute?

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

Question 57

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:

Referring to Instruction 3-1,calculate the arithmetic mean age of the uninsured senior citizens to the nearest hundredth of a year.

Question 58

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 59

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 60

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 61

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

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.

Referring to Instruction 3-2,the coefficient of variation of the carbohydrate amounts is ________ percent.

Question 63

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.
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 64

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.

Referring to Instruction 3-2,the median carbohydrate amount in the cereal is ________ grams.

Question 65

The ________ measures the total spread of the data.

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.

Referring to Instruction 3-2,the standard deviation of the carbohydrate amounts is ________ grams.

Question 67

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.
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 68

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 69

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.
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 70

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.

Referring to Instruction 3-2,construct a box and whisker plot for the carbohydrate amounts.

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.
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 72

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

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.

Referring to Instruction 3-2,what type of shape does the distribution of the sample appear to have?

Question 74

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.

Referring to Instruction 3-2,the range in the carbohydrate amounts is ________ grams.

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.
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.

Referring to Instruction 3-2,the variance of the carbohydrate amounts is ________ (grams squared).

Question 77

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.

Referring to Instruction 3-2,the third quartile of the carbohydrate amounts is ________ grams.

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.

Referring to Instruction 3-2,the first quartile of the carbohydrate amounts is ________ grams.

Question 79

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.

Referring to Instruction 3-2,the arithmetic mean carbohydrates in this sample is ________ grams.

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.

Referring to Instruction 3-2,the interquartile range in the carbohydrate amounts is ________ grams.