Deck 5: Z-Scores and Other Standard Scores

Question 1

Which of the following statements is NOT true regarding z-scores?

A) They describe an average amount that an entire distribution of scores deviates from the mean.
B) They describe how far a particular raw score deviates from the mean.
C) They are in standard deviation units.
D) Negative z-scores reflect deviations below the mean.

Answer 1

A

Question 2

The mean of a z-score distribution is

A) 10.
B) 5.
C) 1.
D) 0.

Answer 2

D

Question 3

The standard deviation of a z-score distribution is

A) 10.
B) 5.
C) 1.
D) 0.

Answer 3

C

Question 4

A z-score is a

A) measure of variability.
B) measure of central tendency.
C) type of standard score.
D) type of raw score.

Question 5

The mean of a z-score distribution is _________ and the standard deviation is __________.

A) 1; 0
B) 0; 1
C) 100; 1
D) 1; 100

Question 6

A z-score provides information about

A) the distribution's overall variability.
B) a person's relative position in a distribution.
C) the most representative value in a distribution.
D) the range of scores in a distribution.

Question 7

If a person earned 98 points on an exam, you can be certain that

A) the person did quite well.
B) the person did quite poorly.
C) the person passed with flying colors.
D) "a" and "c" are both true.
E) more information is needed.

Question 8

A distribution has μ = 40 and σ= 5. Yan scored two standard deviations above the mean. Yan's score was ________.

A) 45
B) 50
C) 55
D) 60

Question 9

If someone obtains a z-score close to 0, that would indicate that

A) the person scored close to the mean.
B) the person scored very low.
C) there was very little variability in the distribution.
D) the person scored better than most.

Question 10

A distribution has a mean of 100 and a standard deviation of 10. Sarah has a z-score of -2.00. What is her raw score?

A) 120
B) 10
C) 90
D) 80

Question 11

An exam has a mean of 75 and a standard deviation of 8. What exam score is 1.5 standard deviations above the mean?

A) 83.5
B) 76.5
C) 87
D) 91

Question 12

In a distribution with μ = 68 and σ = 4, Curtis scored two standard deviations above the mean. His raw score is ________.

A) 70
B) 72
C) 74
D) 76

Question 13

The numerator in the formula for a z-score is

A) a deviation score.
B) the standard deviation.
C) SS
D) ∑X²

Question 14

The denominator in the formula for a z-score is

A) a deviation score.
B) the standard deviation.
C) SS
D) ∑X²

Question 15

A person's raw score is 6 points below the mean and has a z-score of -2. What is the standard deviation for that distribution?

A) 12
B) 9
C) 3
D) -12

Question 16

A distribution has a mean of 36 and a standard deviation of 2.5. Jeremy scored 32. What is his z-score?

A) -.63
B) 63
C) -1.6
D) 1.6

Question 17

A distribution has a mean of 50 and a standard deviation of 10. Robin scored 35. What is her equivalent z-score?

A) -1.5
B) -15
C) -.67
D) -2

Question 18

If we wanted to see a person's relative standing from scores on two different tests,

A) we would compare the person's raw scores to the means of each distribution.
B) both of the person's raw scores would have to be transformed into z-scores.
C) the standard deviations would have to be the same for both distributions.
D) It cannot be done if the means and standards deviations are different for each distribution.

Question 19

If a person has a z-score of -2.00, this would mean that they

A) scored two points higher than the mean.
B) scored two standard deviations above the mean.
C) scored two points lower than the mean.
D) scored two standard deviations below the mean.

Question 20

A distribution has a μ = 46 and a σ = 4. What is the equivalent raw score for a person with a z-score of 1.5?

A) 54
B) 52
C) 50
D) 40

Question 21

Which of the following z-scores is closest to the mean?

A) -.10
B) +.12
C) -1.00
D) +1.00

Question 22

Which of the following z-scores is furthest away from the mean?

A) -1.00
B) 0
C) -.50
D) +2.00

Question 23

A set of scores has a standard deviation of 6. A raw score of 53 converts to a z-score of -1.5. What is the mean of the distribution?

A) 56
B) 62
C) 65
D) 51.5

Question 24

A set of scores has a σ = 4. Susan's score was 93 which converted to a z-score of +2.00. What was the mean of the distribution?

A) 77
B) 81
C) 85
D) 89

Question 25

Hans scored 16 points above the mean with a z-score of +2.00. What was the standard deviation for the distribution?

A) 8
B) 14
C) 18
D) 32

Question 26

A set of scores has a mean of 75. Jiang's score of 60 converted to a z-score of -1.5. What was the standard deviation of the distribution?

A) 5
B) 10
C) 15
D) 20

Question 27

A set of scores has a mean of 36 and a standard deviation of 6. Karim's z-score was -1.50. What was his raw score?

A) 30
B) 24
C) 27
D) 34.5

Question 28

Julie's z-score was +2.50 in a distribution whose μ = 100 with a σ = 10. What was Julie's raw score?

A) 102.5
B) 110
C) 115
D) 125

Question 29

A set of scores has a μ = 65 and a σ = 12. Lucinda's z-score was +1.50. What was her raw score?

A) 53
B) 77
C) 83
D) 89

Question 30

Elijah's z-score was -.25 in a distribution where the mean was 70 and the standard deviation was 8. What is his raw score?

A) 68
B) 65
C) 69.75
D) 72

Question 31

The WAIS has a mean of 100 and a standard deviation of 15. One of the requirements to become a member of MENSA, an organization for smart people, is to score a minimum of two standard deviations above the mean on this test. What is the minimum score requirement?

A) 120
B) 130
C) 145
D) 150

Question 32

Which of the following statistics would be helpful for comparing the scores from two different distributions?

A) range
B) interquartile range
C) standard deviation
D) z-score

Question 33

The mean for a statistics exam was 85. Karen calculated her own z-score to be +1.75 for her test result of 68 points. What is wrong with Karen's calculation?

A) A z-score cannot be calculated for ratio level data.
B) A z-score cannot be calculated for individual score results.
C) Her z-score should be negative.
D) Not enough information is provided.

Question 34

Jorge scored 70 on an exam and his z-score was -2.00. Michelle scored 82 on the same test and her z-score was +1.00. What was the mean of the exam?

A) 74
B) 78
C) 84
D) Not enough information is provided.

Question 35

Isabelle scored 98 on an exam and her z-score was +3.00. Isaac scored 80 on the same exam and his z-score was -3.00. What was the mean of the exam?

A) 89
B) 92
C) 93
D) 86

Question 36

If one z-score from a distribution is -1 for a raw score of 66 and another z-score is +3 for a raw score of 78, what is the standard deviation for the distribution?

A) 2
B) 4
C) 3
D) 6

Question 37

Ariana's raw score of 33 on her philosophy exam converted to a z-score of -1.50. Claire's raw score on the same exam was 48 and it converted to a z-score of +1.00. What was the standard deviation for the distribution?

A) 3
B) 6
C) 9
D) Not enough information is provided.

Question 38

You scored at the mean on your statistics exam. What is your z-score?

A) 0
B) 100
C) +1.00
D) Not enough information is provided.

Question 39

To change a raw score to a z-score, you need to

A) specify a new mean and standard deviation.
B) convert all of the raw scores into z-scores.
C) use the TSS formula.
D) know the mean and standard deviation of the distribution.

Question 40

To use the TSS formula,

A) raw scores have to first be converted to z-scores.
B) a mean has to be specified.
C) a standard deviation has to be specified.
D) All of the above are true.

Question 41

Amar's raw score of 80 converted to a standard score of +1.63. In terms of location in the distribution,

A) Amar's standard score will be +1.63 standard deviations above 80.
B) Amar's standard score and his raw score will be at the same location in the distribution.
C) Amar's raw score will be 1.63 standard deviations above the mean of the distribution.
D) Both "a" and "b" are correct.
E) Both "b" and "c" are correct.

Question 42

Briefly define the following terms:
a. z-score
b. Standard score
c. Transformed standard score

Question 43

Olivia's score was 75 on both her government and history exams. The class mean for the government exam was 80 with a standard deviation of 5. The class mean for the history exam was 70 with a standard deviation of 4. Calculate Olivia's z-scores. On which exam did she perform better?

Question 44

The average weight of a popular brand of snack crackers is 12.4 ounces with a standard deviation of .3 ounce. The box you purchase weighs 12.8 ounces. What is the z-score for your box of crackers?

Question 45

Colby's speed was 24 minutes for his most recent 5K race and his z-score was -2.00. The standard deviation for the race was 4 minutes. What was the mean?

Question 46

Three friends, who are also very competitive, enrolled in three different sections of the same history course. Their raw scores on the first test, along with the means and standard deviations of their respective sections, are listed below.
a. Who gets bragging rights? Explain.
b. Who should devise a new study strategy? Explain.

Question 47

As a part of learning how to administer various tests, students taking a course in psychological measurement were administered the Wechsler IQ test. The mean for the course was 106 and the standard deviation was 11. The scores are listed below for three students. What are their equivalent standardized Wechsler IQ scores?
a. Student One: X = 98
b. Student Two: X = 108
c. Student Three: X = 110

Question 48

Wayne is developing a new assessment instrument, called HOPE, designed to measure peoples' degree of optimism. He will standardize the test with a mean of 75 and a standard deviation of 8. As a preliminary measure, Wayne administers the HOPE scale to a group of volunteers. The mean for the group was 110 and the standard deviation was 6. The scores for two of the volunteers are below.
a. Rylee scored 107. What was her HOPE score?
b. Haru scored 115. What was his HOPE score?

Question 49

A set of population scores along with some summary information is listed below.
a. What is the z-score for a raw score of 8?
b. What is the z-score for a raw score of 3?

Question 50

Given the following quiz scores: 10, 9, 8, 7, 6
a. What is the z-score for a raw score of 7?
b. What is the z-score for a raw score of 10?

Question 51

A set of scores has a mean of 58.23 and a standard deviation of 3.12. Lilly scored -.83 standard deviations below the mean and Karina scored 1.53 standard deviations above the mean.
a. What was Lilly's raw score?
b. What was Karina's raw score?