Deck 2: Describing the Distribution of a Single Variable

Question 1

Numerical variables can be subdivided into which two types?

A)Diverse and categorical
B)Discrete and continuous
C)Nominal and progressive
D)Cross-sectional and discrete

Answer 1

B

Question 2

The difference between the first and third quartile is called the

A)interquartile range
B)interdependent range
C)unimodal range
D)bimodal range
E)mid range

Answer 2

A

Question 3

Gender and State are examples of which type of data?

A)Discrete data
B)Continuous data
C)Categorical data
D)Ordinal data

Answer 3

C

Question 4

A histogram that has a single peak and looks approximately the same to the left and right of the peak is called:

A)bimodal
B)symmetric
C)balanced
D)proportional

Question 5

For a boxplot,the vertical line inside the box indicates the location of the

A)mean
B)median
C)mode
D)minimum value
E)maximum value

Question 6

For a boxplot,the point inside the box indicates the location of the

A)mean
B)median
C)minimum value
D)maximum value

Question 7

Which of the following indicates how many observations fall into various categories?

A)The Likert scale
B)The frequency table
C)The sample table
D)The tabulation scale

Question 8

The median can also be described as:

A)the middle observation when the data values are arranged in ascending order
B)the second quartile
C)the 50^th percentile
D)All of these options

Question 9

A sample of a population taken at one particular point in time is categorized as:

A)categorical
B)discrete
C)cross-sectional
D)time-series

Question 10

If data is stored in a database package,which of the following terms are typically used?

A)Fields and records
B)Cases and columns
C)Variables and samples
D)Variables and observations

Question 11

A histogram that is positively skewed is also called

A)skewed to the right
B)skewed to the left
C)balanced
D)symmetric

Question 12

Data that arise from counts are called:

A)continuous data
B)nominal data
C)counted data
D)discrete data

Question 13

A variable is classified as ordinal if:

A)there is a natural ordering of categories
B)there is no natural ordering of categories
C)the data arise from continuous measurements
D)we track the variable through a period of time

Question 14

Researchers may gain insight into the characteristics of a population by examining a

A)mathematical model describing the population
B)sample of the population
C)description of the population
D)replica

Question 15

Which of the following are the two most commonly used measures of variability?

A)Variance and median
B)Variance and standard deviation
C)Mean and variance
D)Mean and range
E)First quartile and third quartile

Question 16

If a value represents the 95^th percentile,this means that

A)95% of all values are below this value
B)95% of all values are above this value
C)95% of the time you will observe this value
D)there is a 5% chance that this value is incorrect
E)there is a 95% chance that this value is correct

Question 17

In order for the characteristics of a sample to be generalized to the entire population,it should be:

A)symbolic of the population
B)typical of the population
C)representative of the population
D)illustrative of the population

Question 18

A histogram that has exactly two peaks is called a

A)unimodal distribution
B)bimodal distribution
C)skewed distribution
D)scatterplot

Question 19

When we look at a time series plot,we usually look for which two things?

A)"Is there an observable trend?" and "Is there a seasonal pattern?"
B)"Is there an observable trend" and "Can we make predictions?"
C)"Is the sample representative?" and "Is there a seasonal pattern?"
D)"Is there an observable trend?" and "Is the trend symmetric?"

Question 20

Which of the following are possible categorizations of data type?

A)Numerical versus categorical (with subcategories nominal,ordinal)
B)Discrete versus continuous
C)Cross-sectional versus time series
D)All of these options
E)Two of these options

Question 21

Categorical variables can be classified as either discrete or continuous.

Question 22

Which of the following statements is true for the following data values: 7,5,6,4,7,8,and 12?

A)The mean,median and mode are all equal
B)Only the mean and median are equal
C)Only the mean and mode are equal
D)Only the median and mode are equal

Question 23

Suppose that a histogram of a data set is approximately symmetric and "bell shaped".Approximately what percent of the observations are within two standard deviations of the mean?

A)50%
B)68%
C)95%
D)99.7%
E)100%

Question 24

Four different shapes of histograms are commonly observed: symmetric,positively skewed,negatively skewed,and bimodal.

Question 25

Which of the following are the three most common measures of central location?

A)Mean,median,and mode
B)Mean,variance,and standard deviation
C)Mean,median,and variance
D)Mean,median,and standard deviation
E)First quartile,second quartile,and third quartile

Question 26

Some histograms have two or more peaks.This is often an indication that the data come from two or more distinct populations.

Question 27

The average score for a class of 30 students was 75.The 20 male students in the class averaged 70.The 10 female students in the class averaged:

A)75
B)85
C)60
D)70
E)80

Question 28

In a histogram,the percentage of the total area which must be to the left of the median is:

A)exactly 50%
B)less than 50% if the distribution is skewed to the left
C)more than 50% if the distribution is skewed to the right
D)between 25% and 50% if the distribution is symmetric and unimodal

Question 29

Data can be categorized as cross-sectional or time series.

Question 30

A frequency table indicates how many observations fall within each category,and a histogram is its graphical analog.

Question 31

Which of the following statements is true?

A)The sum of the deviations from the mean is always zero
B)The sum of the squared deviations from the mean is always zero
C)The range is always smaller than the variance
D)The standard deviation is always smaller than the variance

Question 32

A sample of 20 observations has a standard deviation of 4.The sum of the squared deviations from the sample mean is:

A)400
B)320
C)304
D)288
E)180

Question 33

A population includes all elements or objects of interest in a study,whereas a sample is a subset of the population used to gain insights into the characteristics of the population.

Question 34

A skewed histogram is one with a long tail extending either to the right or left.The former is called negatively skewed,and the later is called positively skewed.

Question 35

Expressed in percentiles,the interquartile range is the difference between the

A)10^th and 60^th percentiles
B)15^th and 65^th percentiles
C)20^th and 70^th percentiles
D)25^th and 75^th percentiles
E)35^th and 85^th percentiles

Question 36

All nominal data may be treated as ordinal data.

Question 37

For a boxplot,the box itself represents what percent of the observations?

A)lower 25%
B)middle 50%
C)upper 75%
D)upper 90%
E)100%

Question 38

Age,height,and weight are examples of numerical data.

Question 39

The length of the box in the boxplot portrays the

A)mean
B)median
C)range
D)interquartile range
E)third quartile

Question 40

The mode is best described as the

A)middle observation
B)same as the average
C)50^th percentile
D)most frequently occurring value
E)third quartile

Question 41

In a positively skewed distribution,the mean is smaller than the median and the median is smaller than the mode.

Question 42

A histogram is said to be symmetric if it has a single peak and looks approximately the same to the left and right of the peak.

Question 43

The number of car insurance policy holders is an example of a discrete random variable

Question 44

Abby has been keeping track of what she spends to rent movies.The last seven week's expenditures,in dollars,were 6,4,8,9,6,12,and 4.The mean amount Abby spends on renting movies is $7.

Question 45

Phone numbers,Social Security numbers,and zip codes are examples of numerical variables.

Question 46

Suppose that a sample of 10 observations has a standard deviation of 3,then the sum of the squared deviations from the sample mean is 30.

Question 47

Both ordinal and nominal variables are categorical.

Question 48

Distribution is a general term used to describe the way data are distributed,as indicated by a frequency table or histogram.

Question 49

The standard deviation is measured in original units,such as dollars and pounds.

Question 50

Assume that the histogram of a data set is symmetric and bell shaped,with a mean of 75 and standard deviation of 10.Then,approximately 95% of the data values were between 55 and 95.

Question 51

Time series data are often graphically depicted on a line chart,which is a plot of the variable of interest over time.

Question 52

The mean is a measure of central location.

Question 53

The value of the standard deviation always exceeds that of the variance.

Question 54

The median is one of the most frequently used measures of variability.

Question 55

A variable (or field)is an attribute,or measurement,on members of a population,whereas an observation (or case or record)is a list of all variable values for a single member of a population.

Question 56

In the term "frequency table," frequency refers to the number of data values falling within each category.

Question 57

The difference between the first and third quartiles is called the interquartile range.

Question 58

Cross-sectional data are data on a population at a distinct point in time,whereas time series data are data collected across time.

Question 59

The length of the box in the boxplot portrays the interquartile range.

Question 60

If a histogram has a single peak and looks approximately the same to the left and right of the peak,we should expect no difference in the values of the mean,median,and mode.

Question 61

How large must a person's salary should be to qualify as an outlier on the high side? How many outliers are there in these data?

Question 62

Explain what would cause the mean to be slightly lower than the median in this case.

Question 63

What salary amount represents the second quartile?

Question 64

The median of a data set with 30 values would be the average of the 15^th and the 16^th values when the data values are arranged in ascending order.

Question 65

Interpret the variance and standard deviation of this sample.

Question 66

Would you conclude that there is a difference between the salaries of women and men in this plant? Justify your answer.

Question 67

Which of the states listed paid their teachers average salaries that are below 75% of all average salaries?

Question 68

Suppose that a sample of 8 observations has a standard deviation of 2.50,then the sum of the squared deviations from the sample mean is 17.50.

Question 69

What are the mean and median scores on this exam?

Question 70

Explain why the mean and median are different.

Question 71

The Republicans claim that the country was better off in 1990 than in 1980,because the average income increased.Do you agree?

Question 72

The value of the mean times the number of observations equals the sum of all of the data values.

Question 73

Are the empirical rule applicable in this case? If so,apply it and interpret your results.If not,explain why the empirical rule is not applicable here.

Question 74

Find the mean,median,standard deviation,first and third quartiles,and the 95^th percentile for family incomes in both years.

Question 75

The difference between the largest and smallest values in a data set is called the range.

Question 76

Which of the states listed paid their teachers average salaries that exceed at least 75% of all average salaries?

Question 77

Generate a boxplot to summarize the data.What does the boxplot indicate?

Question 78

There are four quartiles that divide the values in a data set into four equal parts.

Question 79

Expressed in percentiles,the interquartile range is the difference between the 25^th and 75^th percentiles.

Question 80

What can you say about the shape of the distributions given the boxplots above?