Deck 4: Central Tendency and Variability

Question 1

The median household income in Albemarle County, Virginia, for the year 2005 was $61,660.If the mean and mode are also computed, which statement could NOT be true?

A) Half of the households had incomes below the median.
B) The majority of households had incomes above the mean.
C) The majority of households had incomes above the median.
D) The majority of households had incomes above the mode.

Answer 1

The majority of households had incomes above the median.

Question 2

The mean of the population is represented by the symbol _____, and the mean of the sample is represented by the symbol _____.

A) M; $\mu$
B) $\mu$ ; M
C) $\mu$ ; $\mu$
D) M; M

Answer 2

$\mu$ ; M

Question 3

At 24 years of age, Megan is 5 feet, 6 inches tall.The national average for height is 5 feet, 4 inches, so Megan is taller than average.The national average is a:

A) population parameter.
B) standardized measure.
C) sum of squares.
D) sample statistic.

Answer 3

population parameter.

Question 4

In a physical geography course, the average score on the first exam was 79 percent based on a sample of 48 students.This mean was calculated on the class grades to summarize overall performance.There are two other sections of the same class, but those students were not included in the calculation.The test average is a:

A) measure of variability.
B) statistic.
C) parameter.
D) mode.

Question 5

Numbers that describe populations are called:

A) statistics.
B) parameters.
C) averages.
D) variables.

Question 6

Six students from a psychology class reported the number of hours of television they watched per week.Here are their data: 18, 12, 15, 14, 13, 16.What is the mean number of hours of television watched per week for this sample of six students?

A) 2.45
B) 6.00
C) 14.50
D) 14.67

Question 7

A marketing specialist for a major department store wants to know how much time people tend to spend in the store so that the audio advertisements will replay on a timed loop, allowing every customer a chance to hear each unique message.What information is this marketing specialist seeking?

A) variability
B) deviation scores
C) central tendency
D) parameter

Question 8

When calculating the median for an odd number of scores, which have been placed in ascending order, the median will be the:

A) middle score.
B) difference between the highest and lowest scores.
C) average of the three scores in the middle.
D) average of the two scores in the middle.

Question 9

Sixteen college freshmen were asked to record the number of alcoholic drinks that they typically consume in a week.Here are their data: 2, 4, 6, 0, 1, 10, 9, 0, 6, 3, 6, 8, 5, 4, 6, 2.What is the median number of alcoholic drinks consumed per week?

A) 4.0
B) 4.5
C) 5.0
D) 5.5

Question 10

The concept of central tendency is best described as:

A) the average.
B) how the data are distributed.
C) the physical middle of our data.
D) the value around which the data seem to gather.

Question 11

Sixteen college freshmen were asked to record the number of alcoholic drinks that they typically consume in a week.Here are their data: 2, 4, 6, 0, 1, 10, 9, 0, 6, 3, 6, 8, 5, 4, 6, 2.What is the mean number of alcoholic drinks consumed per week?

A) 4.50
B) 4.94
C) 5.20
D) 6.00

Question 12

Here is a set of data: 31, 54, 26, 42, 39, 45, 38, 42.What is the mean?

A) 26.00
B) 28.00
C) 39.63
D) 52.84

Question 13

The mean is calculated by:

A) determining the midpoint of the scores in the data set, such that half fall above the mean and half fall below.
B) summing all of the scores in a data set and then dividing by the total number of scores.
C) subtracting the lowest score from the highest score in the data set.
D) determining the most common score in a data set.

Question 14

Here is a set of data: 31, 54, 26, 42, 39, 45, 38, 42.What is the median?

A) 28.0
B) 40.5
C) 42.0
D) 54.0

Question 15

In a physical geography course, the average score on the first exam across all sections of the course was 77.63 percent.Because all students were included in the calculation, the mean is assumed to be based on population data.The test average may be considered to be a:

A) measure of variability.
B) statistic.
C) parameter.
D) mode.

Question 16

The median is the number that perfectly balances the:

A) number of scores in the data set, such that half fall above the median and half fall below the median.
B) deviations of the scores from the mean, such that the sum of the deviations for scores above the mean exactly equals the sum of the deviations for scores below the mean.
C) two most extreme scores in the data set.
D) even and the odd scores in the data set.

Question 17

A sample of 150 women results in an average weight calculation of 168 pounds.This average weight is a:

A) population parameter.
B) standardized measure.
C) sum of squares.
D) sample statistic.

Question 18

Six students from a psychology class reported the number of hours of television they watched per week.Here are their data: 18, 12, 15, 14, 13, 16.What is the median number of hours of television watched per week for this sample of six students?

A) 12.0
B) 14.0
C) 14.5
D) 18.0

Question 19

Here is a set of data: 31, 54, 26, 42, 39, 45, 38, 42, 47.What is the median?

A) 28.0
B) 40.5
C) 42.0
D) 54.00

Question 20

Numbers that describe samples are called:

A) statistics.
B) parameters.
C) averages.
D) variables.

Question 21

Here is a set of scores: 18, 99, 14, 16, 31, 43, 12, 14, 13, 51, 12.Which score is considered to be an outlier?

A) 12
B) 14
C) 51
D) 99

Question 22

Around the end-of-year holidays, such as Thanksgiving, a great amount of meat is purchased.To be prepared for the increased demand, a local grocery store manager wants to know the typical amount of ham sold at medium-sized stores around Thanksgiving.But even more than that, he wants to know how sales tend to vary around that typical amount because he wants to be prepared to sell as many hams as possible.His interest in how much sales vary will require a measure of:

A) central tendency.
B) variability.
C) parameters.
D) statistics.

Question 23

The concept of variability is best described as:

A) the spread of the distribution of data.
B) the lack of consistency in data values.
C) the average deviation of the data.
D) how data tend to cluster around a center.

Question 24

In a sample of data that has several extremely high scores, creating positive skew, the mean will be _____ the median.

A) less than
B) greater than
C) equal to
D) double

Question 25

Professor Kellogg calculates the grades on the first exam for her statistics class.She finds that students did either really well or really poorly.What kind of distribution does Prof.Kellogg have?

A) normal
B) unimodal
C) bimodal
D) negatively skewed

Question 26

In a distribution that is skewed by a few extreme outliers, what would be the best choice for a measure of central tendency?

A) median
B) mode
C) mean
D) range

Question 27

Katrina observes and records the number of people who purchase a meal at the school cafeteria during each operating hour.The cafeteria is open from 6:00 a.m.to 9:00 p.m.and students typically eat breakfast, lunch, and dinner.What type of distribution should Katrina expect to see in her data?

A) normal
B) unimodal
C) bimodal
D) multimodal

Question 28

A multimodal distribution has _____ mode(s).

A) one
B) two
C) two or more
D) more than two

Question 29

In a sample of data that has several extremely low scores, creating negative skew, the mean will be _____ the median.

A) less than
B) greater than
C) equal to
D) double

Question 30

The median is preferred over the mean for _____ distributions.

A) normal
B) unimodal
C) skewed
D) symmetrical

Question 31

A bimodal distribution has _____ mode(s).

A) one
B) two
C) two or more
D) more than two

Question 32

If you knew nothing about your data except that it is a scale variable, which measure of central tendency would be the "safest bet"?

A) mode
B) median
C) mean
D) center

Question 33

In a sample of data that has several extremely high scores, creating positive skew, the mean:

A) will be less than the mode.
B) will be greater than the median.
C) and the mode will be equal.
D) will be less than the median.

Question 34

_____ is affected by outliers because it takes the actual value of each data point into consideration.

A) Mode
B) Median
C) Mean
D) Center

Question 35

A unimodal distribution has _____ mode(s).

A) one
B) two
C) two or more
D) more than two

Question 36

If you wanted to know whether judges in your state are typically male or female, what measure of central tendency would you use to describe the typical judge?

A) mean
B) median
C) mode
D) range

Question 37

The most frequently occurring score in a distribution is the:

A) mean.
B) median.
C) mode.
D) sample statistic.

Question 38

In a sample of data that has several extremely low scores, creating negative skew, the mean:

A) will be greater than the mode.
B) will be greater than the median.
C) and the mode will be equal.
D) will be less than the median.

Question 39

Sixteen college freshmen were asked to record the number of alcoholic drinks they typically consume in a week.Here are their data: 2, 4, 6, 0, 1, 10, 9, 0, 6, 3, 6, 8, 5, 4, 6, 2.What is the mode of this distribution?

A) 2
B) 4
C) 4.5
D) 6

Question 40

Here is a set of data: 31, 54, 26, 42, 39, 45, 38, 42.What is the mode?

A) 39.63
B) 40.50
C) 42.00
D) 54.00

Question 41

Sixteen college freshmen were asked to record the number of alcoholic drinks they typically consume in a week.Here are their data: 2, 4, 6, 0, 1, 10, 9, 0, 6, 3, 6, 8, 5, 4, 6, 2.What is the variance of the number of alcoholic drinks consumed per week?

A) 2.96
B) 3.26
C) 8.75
D) 12.25

Question 42

A standard deviation is equal to 5.50.This number means that the numbers in the sample deviate, on the average:

A) 2.25 units from the mean.
B) 5.50 units from each other.
C) 5.50 units from the mean.
D) 5.50 units from the two extreme scores.

Question 43

If an extreme score is added to a data set, increasing the range of data, the standard deviation will:

A) get closer to 0.
B) decrease.
C) increase.
D) double.

Question 44

Six students from a psychology class reported the number of hours of television they watch per week.Here are their data: 18, 12, 15, 14, 13, 16.The variance of the number of hours of television watched per week for this sample of six students is:

A) 1.97.
B) 3.89.
C) 15.13.
D) 23.33.

Question 45

If the standard deviation of some data is 0.347, what is the variance?

A) 0.35
B) 0.12
C) 0.69
D) It is impossible to determine the variance based on the information provided.

Question 46

Six students from a psychology class reported the number of hours of television they watch per week.Here are their data: 18, 12, 15, 14, 13, 16.What is the standard deviation of the number of hours of television watched per week for this sample of six students?

A) 1.97
B) 3.89
C) 14.67
D) 23.33

Question 47

If the standard deviation of some data is 4.19, what is the range?

A) 0.93
B) 0.89
C) 0.74
D) It is impossible to determine the range based on the information provided.

Question 48

Here is a set of data: 44, 52, 51, 37, 49, 55, 48, 39.Compute a deviation score for the data point 51.

A) 0
B) 4.13
C) 15.00
D) 46.88

Question 49

Which set of scores has the least amount of variability?

A) 22, 26, 21, 23
B) 32, 72, 86, 100
C) 5, 18, 62, 78
D) 101, 110, 56, 13

Question 50

The mean is the measure of central tendency that conveys the mathematical center of the data.

Question 51

If the variance of some data is 26.84, what is the standard deviation?

A) 5.18
B) 8.95
C) 10.36
D) It is impossible to determine the standard deviation based on the information provided.

Question 52

Here is a set of data: 44, 52, 51, 37, 49, 55, 48, 39.Compute a deviation score for the data point 44.

A) -4.16
B) -2.88
C) 0.62
D) 1.74

Question 53

We _____ when calculating the average of deviations from the mean, because the sum of all deviation scores around the mean equals zero.

A) take the absolute value of the scores
B) square the scores
C) divide by N
D) take the square root

Question 54

A researcher analyzed the results of her data and calculated the standard deviation of scores at 6.7.What is the variance?

A) 2.59
B) 6.70
C) 13.40
D) 44.89

Question 55

Sixteen college freshmen were asked to record the number of alcoholic drinks they typically consume in a week.Here are their data: 2, 4, 6, 0, 1, 10, 9, 0, 6, 3, 6, 8, 5, 4, 6, 2.What is the range of this distribution?

A) 0 to 10
B) 2
C) 9
D) 10

Question 56

The _____ is the difference between the lowest and highest scores in the distribution.

A) standard deviation
B) range
C) variance
D) outlier

Question 57

Here is a set of data: 31, 54, 26, 42, 39, 45, 38, 42.What is the range?

A) 26
B) 28
C) 42
D) 54

Question 58

A researcher analyzed the results of her data and calculated the variance of scores at 113.00.What is the standard deviation?

A) 10.63
B) 21.26
C) 56.50
D) 113.00

Question 59

If the variance for a sample is computed and it is found to be rather large, the numbers in the sample are:

A) tightly packed at one extreme.
B) tightly packed around the mean.
C) spread out around the mean.
D) close to the extremes of the distribution.

Question 60

Variance is the average of deviations around the mean expressed in _____ units.

A) standardized
B) absolute value
C) squared
D) logarithmic

Question 61

Compared to the interquartile range, the range is less susceptible to the influence of outliers.

Question 62

It is easier to distort and lie with the mean than with the median.

Question 63

The mean is an appropriate measure of center when considering nominal data.

Question 64

The mean is the measure of central tendency that conveys the middle score of the data.

Question 65

Numbers based on populations are called statistics.

Question 66

It is easier to distort and lie with the median than with the mean.

Question 67

The mode is an appropriate measure of center when considering nominal data.

Question 68

The interquartile range measures variability as the difference between the scores at the 25th and 50th percentiles.

Question 69

The standard deviation is equal to the square root of the variance.

Question 70

The range is less susceptible to the influence of outliers than other measures of variability.

Question 71

The interquartile range measures variability as the difference between the scores at the 75th and 25th percentiles.

Question 72

Mark is looking at distance estimates of where participants think cities are located on a map.Since the estimates are given by x, y coordinates, Mark thinks he should use the mode as a measure of central tendency.What other measures of central tendency are also available?

A) median and mean
B) median and outliers
C) range and sum of squares
D) outliers and mean

Question 73

The interquartile range measures variability as the difference between the scores at the 25th and 100th percentiles.

Question 74

The range is more susceptible to the influence of outliers than other measures of variability.

Question 75

The sum of squares is symbolized as $\\ \Sigma$ .

Question 76

The standard deviation is expressed in squared units.

Question 77

The median is the measure of central tendency that conveys the mathematical center of the data.

Question 78

The sum of squares is symbolized as SD.

Question 79

The most common measure of variability reported in research articles is the standard deviation.

Question 80

The median is preferred over the mean for skewed distributions.