Deck 2: Describing the Distribution of a Variable

Question 1

A histogram is used to display categorical data.

Answer 1

True

Question 2

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

Answer 2

True

Question 3

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

Answer 3

True

Question 4

Categorical variables can be classified as either discrete or continuous.

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

Both ordinal and nominal variables are categorical.

Question 10

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

Question 11

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 12

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 13

Two common ways of displaying categorical data is column charts and pie charts.

Question 14

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 15

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

Question 16

All nominal data may be treated as ordinal data.

Question 17

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 18

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

Question 19

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

Question 20

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

Question 21

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

Question 22

Because they represent such extreme values,outliers should always be eliminated from statistical analyses.

Question 23

The core purpose of time series graphs is to detect historical patterns in the data.

Question 24

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

Question 25

If a 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 will be between 55 and 95.

Question 26

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

Question 27

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

A)symbolic of
B)opposite of
C)representative of
D)different from

Question 28

A sample of 8 observations with a sample standard deviation of 2.50 has a sample variance of 17.50.

Question 29

Coding males as 1 and females as 0 in a data set illustrates the use of _____ variables.

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

Question 30

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

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

Question 31

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

Question 32

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

Question 33

Abby has been keeping track of what she spends to stream movies.The last seven week's expenditures,in dollars,were 6,4,8,9,6,12,and 4.The mean amount Abby spent streaming movies over these 7 weeks is $7.

Question 34

The mean is a measure of central tendency.

Question 35

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

Question 36

A sample,selected from a population,taken at one particular point in time is categorized as

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

Question 37

Gender and states of residence are examples of ____ data.

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

Question 38

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

Question 39

Time series graphs chart the values of one or more time series,using time on the vertical axis.

Question 40

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

Question 41

Which measure of variability is defined as the maximum value of a data set minus the minimum value of a data set?

A)Variance
B)Standard deviation
C)Interquartile range
D)Range

Question 42

The mean of a data set is 75 and one observation has the value of 65.What is the squared deviation of the observation,65,from the mean?

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

Question 43

Which of the following characteristics can be used to describe the skewness of a distribution?

A)The mean
B)Kurtosis
C)The median
D)The standard deviation

Question 44

The length of the box in the box plot portrays the

A)mean.
B)median.
C)range.
D)interquartile range.

Question 45

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

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

Question 46

The mode is best described as the

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

Question 47

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 variability in a skewed distribution.
C)second percentile.
D)the average of all values.

Question 48

The difference between the first and third quartile is called the

A)interquartile range.
B)range.
C)standard deviation.
D)variance.

Question 49

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 50

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

Question 51

Categorizing a numeric age variable as "young," "middle-aged," and "elderly" is an example of

A)counting.
B)ordering.
C)quantifying.
D)binning.

Question 52

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

A)Column chart
B)Histogram
C)Two-way table
D)Pie chart

Question 53

A variable is classified as ordinal if

A)there is a natural ordering of categories.
B)the data is randomly selected.
C)the data arise from continuous measurements.
D)we track the variable through a period of time.

Question 54

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 55

If a value represents the 95^th percentile,this means that 95% of all values in the data set are _____this value.

A)less than or equal to
B)greater than
C)less than
D)greater than or equal to
E)different than

Question 56

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%

Question 57

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

A)the same as
B)greater than
C)significantly less than
D)little less than

Question 58

If the number of observations in a single-variable data set is even,the median is the

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

Question 59

A histogram that is positively skewed may also be described as

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

Question 60

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

A)Lower 25%
B)Middle 50%
C)Upper 75%
D)Upper 90%

Question 61

Where will you find "time" on a time series graph?

A)horizontal axis
B)first column
C)vertical axis
D)last column

Question 62

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

Question 63

Researchers are conducting a review of the "war against poverty" in the latter half of the twentieth century.As part of their analysis,the proportion of Americans under the age of 18 who lived below the poverty line for each of the years 1959 through 2000 is used to generate the following time series plot.
​ How successful was the United States in its efforts to win "the war against poverty" during the 90's?

Question 64

Without performing any calculations,which of the following data sets has the greatest sample standard deviation?

A)1,2,3,4,5,6
B)1,1,3,5,5,6
C)3,3,3,3,3,3
D)1,1,1,5,5,5
E)1,1,3,3,6,6

Question 65

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 66

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

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

Question 67

In a box plot,the asterisk inside the box indicates the location of the

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

Question 68

A political figure running for re-election claimed that the country was better off in 2014 than in 2019,because the average income decreased.Do you agree?

Question 69

In a box plot,the vertical line inside the box indicates the location of the

A)mean.
B)median.
C)mode.
D)standard deviation.

Question 70

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

Question 71

Generate parallel box plots to summarize the data.What do the box plots indicate?

Question 72

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

Question 73

An operations management professor is interested in how her students performed on her midterm exam.The histogram shown below represents the distribution of exam scores (where the maximum score is 100)for 50 students.
​ ​
Based on this histogram,how would you characterize the students' performance on this exam?