Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 5.5 | Other Standardized Distributions Based on z-Scores 145
LEARNING CHECK
1. A population with μ = 85 and σ = 12 is transformed into z-scores. After the
transformation, the population of z-scores will have a standard deviation of _____
a. σ = 12
b. σ = 1.00
c. σ = 0
d. cannot be determined from the information given
2. A population has μ = 50 and σ = 10. If these scores are transformed into
z-scores, the population of z-scores will have a mean of ____ and a standard
deviation of ____.
a. 50 and 10
b. 50 and 1
c. 0 and 10
d. 0 and 1
3. Which of the following is an advantage of transforming X values into z-scores?
a. All negative numbers are eliminated.
b. The distribution is transformed to a normal shape.
c. All scores are moved closer to the mean.
d. None of the other options is an advantage.
ANSWERS
1. B, 2. D, 3. D
5.5 Other Standardized Distributions Based on z-Scores
LEARNING OBJECTIVE
6. Use z-scores to transform any distribution into a standardized distribution with a
predetermined mean and a predetermined standard deviation.
■ Transforming z-Scores to a Distribution
with a Predetermined μ and σ
Although z-score distributions have distinct advantages, many people find them cumbersome
because they contain negative values and decimals. For this reason, it is common
to standardize a distribution by transforming the scores into a new distribution with a
predetermined mean and standard deviation that are whole round numbers. The goal is
to create a new (standardized) distribution that has “simple” values for the mean and
standard deviation but does not change any individual’s location within the distribution.
Standardized scores of this type are frequently used in psychological or educational testing.
For example, raw scores of the Scholastic Aptitude Test (SAT) are transformed to
a standardized distribution that has μ = 500 and σ = 100. For intelligence tests, raw
scores are frequently converted to standard scores that have a mean of 100 and a standard
deviation of 15. Because most IQ tests are standardized so that they have the same mean
and standard deviation, it is possible to compare IQ scores even though they may come
from different tests.