Deck 2: The Mean, Variance, Standard Deviation, and Z Scores

Question 1

A researcher observes the level of aggression of six 5-year-old boys over the course of a school day. The number of incidents for the group of boys was 2, 4, 6, 12, 8, 10. What is the mean number of aggressive acts for this group of children?

A)4
B)5
C)7
D)9

Answer 1

7

Question 2

The ordinary average of a group of numbers is called the __________.

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

Answer 2

mean

Question 3

Which statement is true for the scores 1, 2, 3, 4, 5, 5, 7, 8, 9, 10, 12, 12, 13?

A)The mode is greater than the median
B)The median is greater than the mean
C)The median is greater than the mode
D)The mode is greater than the mean

Answer 3

The median is greater than the mode

Question 4

What is the median of the following scores: 4, 4, 6, 7, 8, 8, 9, 10, 11, 2, 1, 4?

A)4
B)5)5
C)6)5
D)8)5

Question 5

A Canadian political scientist discovers that the number of members of their provincial parliament that a group of voters can name is as follows: 3, 3, 3, 4, 4, 5, 6, 7, 8, 9, 10, 35. Upon examination of these scores, the researcher would probably decide to use which measure of the typical value?

A)Mean
B)Median
C)Mode
D)Standard deviation

Question 6

Five people's scores on a survey of product recognition are 17, 12, 20, 13, 8. What is their mean score?

A)12
B)13
C)14
D)10

Question 7

What is the mode of the following scores: 3, 4, 6, 7, 10, 10, 30, 10, 30, 4, 3, 8 ?

A)3
B)4
C)8)5
D)10

Question 8

A research team studied the rate at which infants in the three different countries vocalized distress. Below are the scores from each country. Which group of infants showed the highest mean rate of distress vocalization over the 45-minute observation period? Country A: 9, 9, 10, 13, 8, 8, 11, 11, 10, 7, 13, 6, 18, 9, 9, 12, 13, 10, 5, 14
Country B: 15, 15, 16, 19, 14, 14, 17, 17, 16, 13, 19, 12, 18, 10, 10, 15, 15, 2, 2, 5
Country C: 4, 6, 20, 17, 15, 30, 18, 18, 25, 2, 29, 17, 16, 35, 19, 1, 30, 25, 16, 15

A)Country A
B)Country B
C)Country C
D)Countries B and C were equal

Question 9

Based on the scores 1, 9, 3, 6, 1, 2, 6, 2, 2, 8, a score of 4 is the __________.

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

Question 10

When a distribution is skewed to the right:

A)the median is greater than the mean
B)the mean and the median are the same
C)the mean is greater than the median
D)the mean and the median are equal

Question 11

The capital Greek letter "sigma" is the symbol for:

A)"average of"
B)"sum of"
C)"variance of"
D)"median of"

Question 12

In a perfectly symmetrical unimodal distribution:

A)there are two values with the highest frequency of scores
B)the mode is slightly less than the mean
C)the mean is larger than the median
D)the mode is the same as the mean

Question 13

The most common single number in a group of scores is the:

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

Question 14

The rule for calculating the mean is to add up all the scores in a sample and divide by the __________.

A)median
B)number of scores minus 1
C)number of scores
D)most frequent score

Question 15

Based on the following scores 1, 2, 3, 4, 5, 6, 8, 8, 8, 9, 10, a score of 8 is the:

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

Question 16

In statistical formulas, what does N stand for?

A)The number of different values possible on the variable
B)The number of scores in a distribution
C)The normal curve
D)The normalized Z score in a distribution of scores

Question 17

The median is greater than the mean in a distribution that is:

A)symmetrical
B)skewed to the right
C)normal
D)skewed to the left

Question 18

The representative value of a group of scores refers to the middle of the group of scores. All of the following are types of representative values EXCEPT:

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

Question 19

The middle value in a set of scores lined up from lowest to highest is the:

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

Question 20

What is the median of the following group of scores: 1, 2, 2, 3, 4, 4, 4, 6, 8, 10?

A)3
B)5)5
C)4
D)3)5

Question 21

Place the five steps for computing variance into the correct order: 1. Divide the sum of squared deviations by the number of scores.
2) Subtract the mean from each score.
3) Add up the squared deviation scores.
4) Compute the mean of the sample.
5) Square each of the deviation scores.

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

Question 22

The mode can be a poor representative value because:

A)it can be difficult to calculate without a statistical software package
B)it does not reflect many aspects of the distribution
C)it is generally larger than the mean
D)all of the above

Question 23

The variance of a group of scores is the same as the:

A)average of the squared deviations from the mean
B)sum of the squared deviations about the mean
C)average of the absolute deviations from the mean
D)sum of the absolute deviations from the median

Question 24

The ________ is the usual way of describing the representative value for a nominal variable such as religious affiliation.

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

Question 25

Measures of variability, such as the variance and standard deviation, are heavily influenced by the presence of one or more:

A)average scores
B)computational formulas
C)variables
D)extreme scores or outliers

Question 26

In a distribution with an even number of scores, the median will be the:

A)most common value
B)average of the two middle scores
C)the median divided by the mean
D)the sum of score divided by N - 1

Question 27

What is the variance of these four scores: 0, 1, 1, 2?

A).25
B).5
C).86
D)1

Question 28

Unless there are __________ , behavioral and social scientists generally use the mean as the measure of the representative value of a group of scores.

A)outliers
B)histograms
C)Z scores
D)two modes

Question 29

The most widely used way of describing the spread of a group of scores is the:

A)range
B)variance
C)square root transformation
D)standard deviation

Question 30

What is the variance of these three scores: 1, 4, 7?

A)3
B)4
C)6
D)9

Question 31

A researcher surveys job satisfaction among laborers and white-collar workers. (Job satisfaction is rated on a scale from 1 = low satisfaction to 10 = high satisfaction.)Results show that laborers have a mean job satisfaction score of 3 and a variance of 1; white-collar workers have a mean job satisfaction rating of 7 and a variance of 10. Which statement best describes what these numbers mean?

A)White-collar workers are less satisfied than laborers.
B)White-collar workers and laborers are about equally satisfied.
C)Laborers generally are less satisfied than white-collar workers, but laborers are just as likely to be highly satisfied as white-collar workers are to be highly dissatisfied.
D)Laborers are less satisfied than white-collar workers and most laborers are about equally dissatisfied while there is more variation in the satisfaction of white-collar workers.

Question 32

In a class of students in which everyone is exactly 24 years old, the variance would be:

A)approximately 1
B)exactly 0
C)between 0 and 1
D)impossible to determine without more information

Question 33

Roughly speaking, the standard deviation is the average amount that scores differ from the:

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

Question 34

In order to compute the range of a group of scores, one must:

A)subtract the lowest score from the highest score
B)multiply the lowest score by the average
C)multiply the highest score by the average
D)subtract the lowest score from the highest and divide by N

Question 35

What is the standard deviation of these four scores: 2, 4, 3, 7?

A)1)87
B)2)35
C)3)50
D)4)05

Question 36

In a distribution of Z scores, the mean is always:

A)10
B)1
C)0
D)50

Question 37

While the mean provides a representative value of a group of scores, it does not tell about the __________.

A)variability of the scores
B)average of the scores
C)spread of the scores around the mean
D)both A and C

Question 38

The variance of a group of scores is 9. What is the standard deviation?

A)1
B)3
C)4)5
D)81

Question 39

The standard deviation of a group of scores is 4. What is the variance?

A)2
B)4
C)8
D)16

Question 40

The standard deviation is defined as the:

A)positive square root of the variance
B)positive square root of the range
C)negative square root of the variance
D)positive square root of the mean or median

Question 41

As compared to a Z score, a raw score is:

A)a transformed score
B)an ordinary score
C)a scaled score
D)a standardized score

Question 42

A researcher studying the sociological implications of cultural diversity conducts lengthy interviews with members of various cultural communities. What kind of method is this sociologist probably using?

A)Behavioral techniques
B)Quantitative techniques
C)Qualitative techniques
D)Positivistic techniques

Question 43

For the questions below: A statistics student (Lee)wants to compare his final exam score to his friend Zoey's final exam score from last year. However, the two exams were scored on different scales. Lee asks Zoey for the mean and standard deviation of her class on the exam as well as her final exam score. Compute the Z scores for Lee and Zoey. Lee: Final exam score = 85; Class: M = 70; SD = 10
Zoey: Final exam score = 45; Class: M = 35; SD = 5

A)Lee, Z = 1.50; Zoey, Z = 2.00
B)Lee, Z = -1.07; Zoey, Z = -1.14
C)Lee, Z = 1.07; Zoey, Z = -1.14
D)Lee, Z = 1.07; Zoey, Z = 1.50

Question 44

The ordinary arithmetic average is called the __________.

Question 45

A research article states that "At the time of the study, the mean age of first-year college students at Wayne University was 17.6 (3.57). The number in parentheses likely represents:

A)the Z score
B)the standard deviation
C)the mode
D)an outlier

Question 46

Although __________ and __________ are often provided in research articles (in the text or tables), _________ are rarely reported.

A)variance, range, Z scores
B)Z scores, T scores, means
C)means, standard deviations, Z scores
D)outliers, Z scores, means

Question 47

A person's raw score is 7, the mean is 13, and the standard deviation is 3. What is the person's Z score?

A)-2
B)-1
C)1
D)2

Question 48

The mean of the scores 2, 2, 2, 6 is __________.

Question 49

Who was the behavioral psychologist opposed to the use of statistics in psychology?

A)Cohen
B)McCracken
C)Cronbach
D)Skinner

Question 50

Donald's score on the statistics test was +1.25. This means that he scored:

A)slightly below the average
B)just at the average
C)a little less than one standard deviation below the mean
D)more than one standard deviation above the mean

Question 51

A raw score is equal to the:

A)Z score multiplied by the standard deviation, plus the mean
B)Z score multiplied by the variance, plus the mean
C)standard deviation multiplied by the mean, plus the variance
D)raw score minus the mean, divided by the variance

Question 52

In relation to the other people in their classes, who had the better exam score?

A)Lee
B)Zoey
C)They were equal
D)It is not possible to say without more information

Question 53

For a particular group of scores, M = 15 and SD = 3. Provide the raw score for a Z score of 7:

A)15
B)24
C)36
D)48

Question 54

A __________ describes a particular score in terms of where it fits into the overall group of scores.

A)standard deviation
B)computational formula
C)Z score
D)Q score

Question 55

For a particular group of scores, M = 20 and SD = 5. What is the Z score for a raw score of 10?

A)2
B)0
C)-2
D)-1

Question 56

A Z score of 2.0 came from a distribution with a mean of 80 and a standard deviation of 10. What is the raw score?

A)82
B)90
C)100
D)170

Question 57

All of the following are true statements about a Z score EXCEPT:

A)it is the number of standard deviations the actual score is above or below the mean
B)it is negative if the actual score falls below the mean
C)it is negative if the actual score falls above the mean
D)it is zero if the actual score falls at the mean

Question 58

Qualitative research techniques are likely to involve each of the following EXCEPT:

A)lengthy interviews
B)focus groups
C)quantitative methods (e.g., statistics)
D)observations of individuals (e.g., in natural settings)

Question 59

Whose name is associated with behaviorism and opposition to the field of statistics on the basis that important information may be lost by averaging the results of a number of cases?

A)James
B)Freud
C)Wolpe
D)Skinner

Question 60

Which of the following is NOT an advantage of Z scores?

A)You can compare scores from scales with different amounts of variation.
B)You can easily tell if a score is above or below the mean.
C)You can easily tell how far above or below the mean a score is.
D)You can easily tell the shape of the scores' distribution.

Question 61

Five high school English teachers were given a grammar test. Their scores were as follows: 17, 19, 14, 20, 20.
Figure the mean, mode, variance, and standard deviation for this sample.
Explain what you have done and what the results mean to a person who has never had a course in statistics.

Question 62

The variance of a group of scores is the average of the __________.

Question 63

A(n)__________ is the number of standard deviations a score is above or below the mean.

Question 64

In statistics, the best measure of the representative value of a group of scores is usually the mode. (True or False)

Question 65

In a perfectly symmetrical unimodal distribution, the mode is the same as the mean. (True or False)

Question 66

The formula for changing a Z score to a raw score is __________.

Question 67

A group of scores is 6, 7, 7, 8, 10, 11. What is N?

Question 68

The __________ is the value with the most scores.

Question 69

The variance of the scores 1, 7, 13 is __________.

Question 70

A group of scores is 2, 2, 4, 8, 9, 25. What is the median?

Question 71

The __________ is approximately the average that a score differs from the mean.

Question 72

A deviation score is the difference between the score and the __________.

Question 73

A group of scores is 6, 18, 4, 21, 22. __________ is the median.

Question 74

A group of scores is 2, 81, 82, 82, 84, 86, 90. The number __________ is an outlier.

Question 75

A group of scores is 2, 2, 4, 8, 9, 2, 10, 15, 30, 30. What is the mode?

Question 76

A teacher rated the reading ability level of six fourth-grade children participating in a special math program. The ratings were as follows: 3, 3, 2, 8, 4, 4.
Figure the mean, variance, and standard deviation for this group of scores.
Explain what you have done and what the results mean to a person who has never had a course in statistics.

Question 77

The standard deviation is the __________ of the variance.

Question 78

A raw score is 28, M = 20, and SD = 2. The Z score is __________.

Question 79

A Z score is -3 and the sample's M = 30 and SD = 6. The raw score is __________.

Question 80

Alex's Z score on his abnormal psychology exam was -.05, indicating that he scored well above the mean on the exam. (True or False).