Deck 2: Describing the Distribution of a Single Variable

Question 1

Researchers may try to gain insight into the characteristics of a population by examining a(n) _____ of the population.

A) model
B) sample
C) exemplar
D) replica

Answer 1

sample

Question 2

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

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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

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

Question 5

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

Question 6

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

Question 7

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 8

Gender and states of residence are examples of ____ data.

A) discrete
B) continuous
C) categorical
D) ordinal

Question 9

A data set is typically a rectangular array of data, with observations in columns and variables in rows.

Question 10

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 11

A variable (or field or attribute) is a characteristic of 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 12

Categorizing age variables as "young," "middle-aged," and "elderly" is an example of:

A) counting
B) ordering
C) value adding
D) binning
E) categorizing

Question 13

Coding males as 1 and females as 0 in a data set illustrates the use of:

A) nominal variables
B) dummy variables
C) numerical variables
D) ordinal variables

Question 14

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 15

Data that arise from counts are best described as _____ data.

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

Question 16

The daily closing values of the Dow Jones Industrial Average over a period of 30 days are best described as _____ data.

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

Question 17

Categorical variables can be classified as either discrete or continuous.

Question 18

Phone numbers, Social Security numbers, and zip codes are typically treated as numerical variables.

Question 19

All nominal data may be treated as ordinal data.

Question 20

Excel^® stores dates as:

A) numbers
B) variables
C) records
D) text

Question 21

What is the most common type of chart for showing the distribution of a numerical variable?

A) time series graph
B) histogram
C) bin
D) box plot

Question 22

Which statement 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

The interquartile range (IQR) encompasses what percent of the observations?

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

Question 24

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 25

What are the three most common measures of central tendency?

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

Indicate the type of data for each of the six variables included in this set.

Question 27

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 28

The length of the box in the box plot portrays the:

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

Question 29

The only meaningful way to summarize categorical data is with counts of observations in the categories.

Question 30

The median can also be described as the:

A) middle observation when the data values are arranged in ascending order
B) best estimate of the population mean based on multiple samples
C) second percentile
D) the average of all values

Question 31

With symmetric, "bell-shaped" distributions, 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 32

Both ordinal and nominal variables are categorical.

Question 33

How is the median defined if the number of observations is even?

A) the average of the two middle observations
B) the difference between the two middle observations
C) the most frequent observation
D) the difference between the highest and smallest observation

Question 34

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 35

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

Question 36

A histogram that is positively skewed is also called:

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

Question 37

As a measure of variability, what is defined as the maximum value minus the minimum value?

A) variance
B) standard deviation
C) mean
D) range
E) median

Question 38

Statistics professor has just given a final examination in his statistical inference course. He is particularly interested in learning how his class of 40 students performed on this exam. The scores are shown below.
What are the mean and median scores on this exam?

Question 39

What measure of distribution relates to extreme events, such as a stock market crash?

A) asymmetric
B) kurtosis
C) negatively skewed
D) skewness

Question 40

Using dummy variables is an efficient way of determining counts of categorical variables.

Question 41

A distribution of a numerical variable with no skewness is said to be symmetric.

Question 42

In an extremely right-skewed distribution, the mean is much smaller than the median.

Question 43

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 44

The mean is a measure of central tendency.

Question 45

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 46

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

Question 47

A distribution with a high kurtosis has almost all of its observations within three standard deviations of the mean.

Question 48

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

Question 49

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 50

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

Question 51

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

Question 52

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

Question 53

If the mean is 75 and two observations have values of 65 and 85, what is the squared deviation of each?

A) 100
B) 20
C) 400
D) 10

Question 54

In the term "frequency table," frequency refers to the counts of observations in specified categories.

Question 55

As a graphical tool, the histogram is ideal for showing whether the distribution of a numerical variable is symmetric or skewed.

Question 56

A histogram is based on binning the variable, which means putting the variable into discrete categories.

Question 57

Unlike histograms, box plots depict only one aspect of a variable.

Question 58

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 59

Mean absolute deviation (MAD) is the average of the squared deviations.

Question 60

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) the same as the males
B) higher than the males
C) significantly lower than the males
D) little lower than the males

Question 61

The data shown below contains family incomes (in thousands of dollars) for a set of 50 families sampled in 2007 and 2017. Assume that these families are good representatives of the entire United States. ​
Find the mean, median, standard deviation, first and third quartiles, and the 95^th percentile for family incomes in both years.

Question 62

A political figure running for re-election claimed that the country was better off in 2017 than in 2007, because the average income increased. Do you agree?

Question 63

What salary amount represents the second quartile?

Question 64

A manager for Marko Manufacturing, Inc. has recently been hearing some complaints that women are being paid less than men for the same type of work in one of their manufacturing plants. The box plots shown below represent the annual salaries for all salaried workers in that facility (40 men and 34 women).
Would you conclude that there is a difference between the salaries of women and men in this plant? Justify your answer.

Question 65

Generate a box plot to summarize the data. What does the box plot indicate?

Question 66

Calculate the interquartile range. What does this tell you about the data?

Question 67

Suppose that an analysis of a set of test scores reveals that: , and
What can you say about the relative position of each of the observations 34, 84, and 104?

Question 68

Suppose that an analysis of a set of test scores reveals that: , and
What do these statistics tell you about the shape of the distribution?

Question 69

How would you describe the salary of Virginia's teachers compared to those across the entire United States? Justify your answer.

Question 70

Compute the mean number of children.

Question 71

Explain why the mean is slightly lower than the median in this case.

Question 72

Below you will find summary measures on starting salaries for classroom teachers across the United States. You will also find a list of selected states and their average starting teacher salary. All values are in thousands of dollars.
Starting salaries for classroom teachers across the United States Selected states and their average starting teacher salary (in thousands of dollars)
Which of the states listed paid their teachers average salaries that exceed at least 75% of all average salaries?

Question 73

Compute the median number of children.

Question 74

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 75

Statistics professor has just given a final examination in his statistical inference course. He is particularly interested in learning how his class of 40 students performed on this exam. The scores are shown below.
Explain why the mean and median are different.

Question 76

Below you will find summary measures on starting salaries for classroom teachers across the United States. You will also find a list of selected states and their average starting teacher salary. All values are in thousands of dollars.
Starting salaries for classroom teachers across the United States Selected states and their average starting teacher salary (in thousands of dollars)
Which of the states listed paid their teachers average salaries that are below 75% of all average salaries?

Question 77

A sample of 8 observations with a standard deviation of 2.50 has a sum of the squared deviations from the sample mean equal to 17.50.

Question 78

What can you say about the shape of the distributions given the accompanying box plots?

Question 79

Are the empirical rules applicable in this case? If so, apply them and interpret your results. If not, explain why the empirical rules are not applicable here.

Question 80

In an effort to provide more consistent customer service, the manager of a local fast-food restaurant would like to know the dispersion of customer service times in relation to their average value for the facility's drive-up window. The table below provides summary measures for the customer service times (in minutes) for a sample of 50 customers collected over the past week.
Interpret the variance and standard deviation of this sample.