,Liberty University PSYC 354 Quiz 3 | Statistics for the
Social Sciences (2026) Q&A
1. Which of the following best describes the purpose of variability in statistics?
A) To identify the most typical score in a distribution
B) To measure the spread or dispersion of scores in a distribution
C) To determine the causal relationship between variables
D) To calculate the probability of an event occurring
Correct Answer: To measure the spread or dispersion of scores in a distribution
Rationale: Variability refers to the extent to which scores in a distribution differ from one
another. It provides information about how spread out or clustered the data are. The three
main measures of variability are the range, variance, and standard deviation.
2. What is the range of the following scores: 12, 15, 18, 20, 25?
A) 10
B) 12
C) 13
D) 15
Correct Answer: 13
Rationale: The range is calculated by subtracting the smallest score from the largest score. In
this dataset, the largest score is 25 and the smallest is 12, so the range is 25 – 12 = 13. The
range is the simplest measure of variability.
3. Why do deviation scores have to be squared before calculating the standard deviation?
A) Squaring is necessary for calculating inferential statistics
,B) If deviation scores are not squared, the average distance from the mean will always equal
zero
C) Squaring deviation scores allows for degrees of freedom to be calculated
D) If deviation scores are not squared, the interquartile range is incalculable
Correct Answer: If deviation scores are not squared, the average distance from the mean will
always equal zero
Rationale: Deviation scores are the distances of each score from the mean. If these
deviations are summed without squaring, the positive and negative deviations cancel each
other out, always resulting in zero. Squaring the deviations eliminates the signs and allows
for a meaningful measure of variability.
4. For a population, a deviation score is computed as which of the following?
A) X + μ
B) X – μ
C) μ – X
D) X × μ
Correct Answer: X – μ
Rationale: A deviation score is the difference between a score (X) and the population mean
(μ). It indicates how far a score is from the mean. The sum of all deviation scores in a
population is always zero, which is why deviations are squared when calculating variance.
5. For a population of scores, the sum of the deviation scores is equal to which of the
following?
A) The mean
B) The variance
C) Zero
D) The standard deviation
, Correct Answer: Zero
Rationale: The sum of deviation scores around the mean is always zero because the mean is
the balance point of the distribution. The positive deviations (scores above the mean) exactly
offset the negative deviations (scores below the mean). This property is fundamental to the
definition of the mean.
6. Which symbol identifies the sample variance?
A) s
B) s²
C) σ
D) σ²
Correct Answer: s²
Rationale: The symbol s² represents the sample variance, which is the average of the squared
deviations from the sample mean. The symbol s represents the sample standard deviation,
while σ² and σ represent the population variance and standard deviation, respectively.
7. The value for SS (sum of squares) can be less than zero.
A) True
B) False
Correct Answer: False
Rationale: The sum of squares (SS) is the sum of squared deviation scores. Because squared
values are always positive or zero, SS can never be less than zero. SS is a measure of total
variability and is used in calculating variance and standard deviation.
8. What is the formula for calculating the sample variance?
A) SS / N
Social Sciences (2026) Q&A
1. Which of the following best describes the purpose of variability in statistics?
A) To identify the most typical score in a distribution
B) To measure the spread or dispersion of scores in a distribution
C) To determine the causal relationship between variables
D) To calculate the probability of an event occurring
Correct Answer: To measure the spread or dispersion of scores in a distribution
Rationale: Variability refers to the extent to which scores in a distribution differ from one
another. It provides information about how spread out or clustered the data are. The three
main measures of variability are the range, variance, and standard deviation.
2. What is the range of the following scores: 12, 15, 18, 20, 25?
A) 10
B) 12
C) 13
D) 15
Correct Answer: 13
Rationale: The range is calculated by subtracting the smallest score from the largest score. In
this dataset, the largest score is 25 and the smallest is 12, so the range is 25 – 12 = 13. The
range is the simplest measure of variability.
3. Why do deviation scores have to be squared before calculating the standard deviation?
A) Squaring is necessary for calculating inferential statistics
,B) If deviation scores are not squared, the average distance from the mean will always equal
zero
C) Squaring deviation scores allows for degrees of freedom to be calculated
D) If deviation scores are not squared, the interquartile range is incalculable
Correct Answer: If deviation scores are not squared, the average distance from the mean will
always equal zero
Rationale: Deviation scores are the distances of each score from the mean. If these
deviations are summed without squaring, the positive and negative deviations cancel each
other out, always resulting in zero. Squaring the deviations eliminates the signs and allows
for a meaningful measure of variability.
4. For a population, a deviation score is computed as which of the following?
A) X + μ
B) X – μ
C) μ – X
D) X × μ
Correct Answer: X – μ
Rationale: A deviation score is the difference between a score (X) and the population mean
(μ). It indicates how far a score is from the mean. The sum of all deviation scores in a
population is always zero, which is why deviations are squared when calculating variance.
5. For a population of scores, the sum of the deviation scores is equal to which of the
following?
A) The mean
B) The variance
C) Zero
D) The standard deviation
, Correct Answer: Zero
Rationale: The sum of deviation scores around the mean is always zero because the mean is
the balance point of the distribution. The positive deviations (scores above the mean) exactly
offset the negative deviations (scores below the mean). This property is fundamental to the
definition of the mean.
6. Which symbol identifies the sample variance?
A) s
B) s²
C) σ
D) σ²
Correct Answer: s²
Rationale: The symbol s² represents the sample variance, which is the average of the squared
deviations from the sample mean. The symbol s represents the sample standard deviation,
while σ² and σ represent the population variance and standard deviation, respectively.
7. The value for SS (sum of squares) can be less than zero.
A) True
B) False
Correct Answer: False
Rationale: The sum of squares (SS) is the sum of squared deviation scores. Because squared
values are always positive or zero, SS can never be less than zero. SS is a measure of total
variability and is used in calculating variance and standard deviation.
8. What is the formula for calculating the sample variance?
A) SS / N
