,Liberty University PSYC 354 Quiz 4 | Statistics for the Social
Sciences (2026) Q&A
1. Which of the following best describes the purpose of transforming raw scores into z-
scores?
A) To change the shape of the distribution to normal
B) To standardize scores so they can be compared across different distributions
C) To eliminate outliers from the data set
D) To increase the magnitude of the mean difference
Correct Answer: To standardize scores so they can be compared across different
distributions
Rationale: A z-score transformation converts raw scores into a standardized distribution with
a mean of 0 and a standard deviation of 1. This allows researchers to compare scores from
distributions that may have different means and standard deviations. It does not alter the
shape of the distribution or remove outliers.
2. Which position in a distribution corresponds to a z-score of z = –1.00?
A) Below the mean by 1 point
B) Below the mean by 1 standard deviation
C) Above the mean by 1 point
D) Above the mean by 1 standard deviation
Correct Answer: Below the mean by 1 standard deviation
Rationale: A z-score represents the distance in standard deviation units. A z-score of z = –
1.00 indicates a score that is exactly 1 standard deviation below the mean of the distribution.
The negative sign indicates the score is below the mean.
3. Which z-score value represents the location farthest from the mean?
,A) z = +0.50
B) z = –0.50
C) z = –1.00
D) z = –2.00
Correct Answer: z = –2.00
Rationale: The absolute value of the z-score indicates the distance from the mean, regardless
of sign. A z-score of z = –2.00 is farthest from the mean because its absolute value (2.00) is
larger than any of the other options. This score is 2 standard deviations below the mean.
4. Under which circumstance is a score that is 15 points above the mean an extreme score
relatively far from the mean?
A) When the population mean is much larger than 15
B) When the population standard deviation is much larger than 15
C) When the population mean is much smaller than 15
D) When the population standard deviation is much smaller than 15
Correct Answer: When the population standard deviation is much smaller than 15
Rationale: A score’s extremity is determined by its z-score, which is the distance from the
mean divided by the standard deviation. If the standard deviation is very small, a 15-point
difference represents many standard deviations, making the score extreme. If the standard
deviation is large, 15 points may be less than one standard deviation.
5. A researcher may decide to transform original scores into a distribution with a pre-
determined mean and standard deviation other than the z-score distribution because the z-
score distribution _____.
A) Often has a standard deviation and mean that is too small
B) Does not allow for comparisons between otherwise different distributions
C) Often contains decimals and negative values
D) Is not standardized
, Correct Answer: Often contains decimals and negative values
Rationale: The z-score distribution often contains decimals and negative values, which can
be cumbersome to work with in some contexts. Transforming scores to a distribution with a
more convenient mean (e.g., 100) and standard deviation (e.g., 15) retains the standardized
properties while producing more manageable numbers. It still allows for comparisons.
6. For a distribution of scores, the location identified by z = +1 and the location identified by
z = –1 are the same distance from the mean.
A) True
B) False
Correct Answer: True
Rationale: A z-score of +1 indicates a score 1 standard deviation above the mean, and a z-
score of –1 indicates a score 1 standard deviation below the mean. Because both represent a
distance of exactly 1 standard deviation, they are equidistant from the mean. The distribution
is symmetric around the mean.
7. One purpose of a z-score is to standardize a score so that it can readily be compared with
scores from other distributions that also have been transformed into z-scores.
A) True
B) False
Correct Answer: True
Rationale: The primary purpose of z-scores is to standardize scores, allowing for meaningful
comparisons across different distributions that may have different means and standard
deviations. By transforming scores to a common scale (mean = 0, SD = 1), researchers can
compare relative standing. This is fundamental to many statistical procedures.
Sciences (2026) Q&A
1. Which of the following best describes the purpose of transforming raw scores into z-
scores?
A) To change the shape of the distribution to normal
B) To standardize scores so they can be compared across different distributions
C) To eliminate outliers from the data set
D) To increase the magnitude of the mean difference
Correct Answer: To standardize scores so they can be compared across different
distributions
Rationale: A z-score transformation converts raw scores into a standardized distribution with
a mean of 0 and a standard deviation of 1. This allows researchers to compare scores from
distributions that may have different means and standard deviations. It does not alter the
shape of the distribution or remove outliers.
2. Which position in a distribution corresponds to a z-score of z = –1.00?
A) Below the mean by 1 point
B) Below the mean by 1 standard deviation
C) Above the mean by 1 point
D) Above the mean by 1 standard deviation
Correct Answer: Below the mean by 1 standard deviation
Rationale: A z-score represents the distance in standard deviation units. A z-score of z = –
1.00 indicates a score that is exactly 1 standard deviation below the mean of the distribution.
The negative sign indicates the score is below the mean.
3. Which z-score value represents the location farthest from the mean?
,A) z = +0.50
B) z = –0.50
C) z = –1.00
D) z = –2.00
Correct Answer: z = –2.00
Rationale: The absolute value of the z-score indicates the distance from the mean, regardless
of sign. A z-score of z = –2.00 is farthest from the mean because its absolute value (2.00) is
larger than any of the other options. This score is 2 standard deviations below the mean.
4. Under which circumstance is a score that is 15 points above the mean an extreme score
relatively far from the mean?
A) When the population mean is much larger than 15
B) When the population standard deviation is much larger than 15
C) When the population mean is much smaller than 15
D) When the population standard deviation is much smaller than 15
Correct Answer: When the population standard deviation is much smaller than 15
Rationale: A score’s extremity is determined by its z-score, which is the distance from the
mean divided by the standard deviation. If the standard deviation is very small, a 15-point
difference represents many standard deviations, making the score extreme. If the standard
deviation is large, 15 points may be less than one standard deviation.
5. A researcher may decide to transform original scores into a distribution with a pre-
determined mean and standard deviation other than the z-score distribution because the z-
score distribution _____.
A) Often has a standard deviation and mean that is too small
B) Does not allow for comparisons between otherwise different distributions
C) Often contains decimals and negative values
D) Is not standardized
, Correct Answer: Often contains decimals and negative values
Rationale: The z-score distribution often contains decimals and negative values, which can
be cumbersome to work with in some contexts. Transforming scores to a distribution with a
more convenient mean (e.g., 100) and standard deviation (e.g., 15) retains the standardized
properties while producing more manageable numbers. It still allows for comparisons.
6. For a distribution of scores, the location identified by z = +1 and the location identified by
z = –1 are the same distance from the mean.
A) True
B) False
Correct Answer: True
Rationale: A z-score of +1 indicates a score 1 standard deviation above the mean, and a z-
score of –1 indicates a score 1 standard deviation below the mean. Because both represent a
distance of exactly 1 standard deviation, they are equidistant from the mean. The distribution
is symmetric around the mean.
7. One purpose of a z-score is to standardize a score so that it can readily be compared with
scores from other distributions that also have been transformed into z-scores.
A) True
B) False
Correct Answer: True
Rationale: The primary purpose of z-scores is to standardize scores, allowing for meaningful
comparisons across different distributions that may have different means and standard
deviations. By transforming scores to a common scale (mean = 0, SD = 1), researchers can
compare relative standing. This is fundamental to many statistical procedures.
