Deck 2: Describing the Distribution of a Single Variable

Question 1

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

Answer 1

True

Question 2

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

Answer 2

False

Question 3

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.

Answer 3

True

Question 4

The count of categories is the only meaningful way to summarize categorical data.

Question 5

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

Question 6

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

Question 7

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 8

All nominal data may be treated as ordinal data.

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

Categorical variables can be classified as either discrete or continuous.

Question 14

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

Question 15

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

Question 16

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

Question 17

The mean is a measure of central tendency.

Question 18

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

Question 19

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

Question 20

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 21

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 22

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 23

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

Question 24

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

Question 25

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 26

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 27

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

Question 28

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

Question 29

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 30

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

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

Question 31

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

Question 32

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

Question 33

A histogram that is positively skewed is also called

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

Question 34

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

Question 35

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

Question 36

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

Question 37

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 38

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

Question 39

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 40

Both ordinal and nominal variables are categorical.

Question 41

The length of the box in the box plot portrays the

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

Question 42

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

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

Question 43

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 44

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 45

The median can also be described as the

A) middle observation when the data values are arranged in ascending order
B) population mean
C) second percentile
D) the average of all values

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
E) third quartile

Question 47

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 48

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 49

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 50

In a generic box plot,the x inside the box indicates the location of the

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

Question 51

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 52

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

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

Question 53

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 54

Gender and State are examples of which type of data?

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

Question 55

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 56

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 57

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

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

Question 58

Data that arise from counts are called

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

Question 59

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

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

Question 60

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 61

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 62

Which of the following 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 63

Excel stores dates as

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

Question 64

The daily closing values of the Dow Jones Industrial Average are examples of

A) cross-sectional data
B) discrete data
C) time-series data
D) continuous data
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
$$\begin{array} { | l l | } \hline & \text { Salary } \\\hline \text { Count } & 51.000 \\\text { Mean } & 35.890 \\\text { Median } & 35.000 \\\text { Standard deviation } & 6.226 \\\text { Minimum } & 26.300 \\\text { Maximum } & 50.300 \\\text { Variance } & 38.763 \\\text { First quartile } & 31.550 \\\text { Third quartile } & 40.050 \\\hline\end{array}$$
Selected states and their average starting teacher
$$\begin{array} { | l l | } \hline \text { State } & \text { Salary } \\\hline \text { Alabama } & 31.3 \\\text { Colorado } & 35.4 \\\text { Connecticut } & 50.3 \\\text { Delaware } & 40.5 \\\text { Nebraska } & 31.5 \\\text { Nevada } & 36.2 \\\text { New Hampshire } & 35.8 \\\text { New Jersey } & 47.9 \\\text { New Mexico } & 29.6 \\\text { South Carolina } & 31.6 \\\text { South Dakota } & 26.3 \\\text { Tennessee } & 33.1 \\\text { Texas } & 32.0 \\\text { Utah } & 30.6 \\\text { Vermont } & 36.3 \\\text { Virginia } & 35.0 \\\text { Wyoming } & 31.6 \\\hline\end{array}$$

Question 65

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 66

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%