PSYC 354 | Statistics for the Behavioral Sciences Module 3 | Variability | 2026 Update
PSYC 354 MODULE 3 QUIZ
Variability | Questions and Answers | 2026 Update | Passed!!
Course PSYC 354 — Statistics for the Behavioral Sciences (Liberty University)
Module 3 Quiz — Variability: Range, IQR, SS, Variance, Standard Deviation &
Assessment
Degrees of Freedom
Total Questions 30 (Multiple Choice, Single Best Answer)
Total Points 100 points (3.33 points per question; Q30 = 3.40 pts)
Cognitive Distribution 30% Recall | 50% Application | 20% Analysis
Format Mix 75% Scenario-Based Calculation & Interpretation | 25% Direct Conceptual
Alignment APA 7th Edition Reporting | 2026–2027 Academic Standards
Range, IQR & Data Spread; SS, Variance & Standard Deviation; Population vs.
Domains Covered Sample Variability, Degrees of Freedom & Behavioral Applications (SPSS/JASP,
MAD, APA 7, AI Screening)
Examiner Directive: This Module 3 examination assesses mastery-level competency in
measures of variability, consistent with the Liberty University PSYC 354 curriculum. Each item
requires absolute mathematical precision, proper statistical notation (σ for population SD, s for
sample SD, σ² and s² for variances, N for population size, n for sample size, SS for sum of
squares, df for degrees of freedom), and foolproof step-by-step rationales. Distractors are
engineered to represent the most common student calculation errors — including dividing by N
instead of n−1 for a sample variance (omitting Bessel's correction), forgetting to square the
deviations in the SS formula, confusing population and sample notation, computing ΣX² instead
of Σ(X−µ)², and mishandling the (ΣX)²/N term in the computational SS formula. The 2026
update integrates contemporary SPSS/JASP variability-table interpretation, robust estimators
such as the Median Absolute Deviation (MAD), modern data visualization (boxplots, violin
plots), AI-assisted outlier screening, and APA 7th-edition reporting standards for variability.
SECTION 1: Fundamentals of Variability — Range, Interquartile
Range, and Data Spread (Q1–Q10)
Q1: Which of the following best defines 'variability' in the context of descriptive
statistics?
A. The central or typical value of a distribution
B. The total number of scores in a data set
C. The degree to which scores in a distribution are spread out or dispersed from each
other and from the central value — providing a quantitative measure of how spread out
the scores are [CORRECT]
D. The probability of obtaining a specific score by chance
Correct Answer: C — C. The degree to which scores in a distribution are spread out or
dispersed from each other and from the central value — providing a quantitative
measure of how spread out the scores are
Page 1 | Complete Solution Key
, PSYC 354 | Statistics for the Behavioral Sciences Module 3 | Variability | 2026 Update
Rationale: Variability (or dispersion) quantifies how spread out or scattered the scores in a
distribution are — how far they deviate from each other and from the central value. Option A
describes central tendency (mean, median, mode), the opposite concept. Option B describes
sample size (N or n). Option D describes probability, not variability. Variability complements central
tendency: together they fully characterize a distribution's shape.
Q2: A clinician records the number of therapy sessions attended by five clients: 3, 7, 4,
9, and 2. What is the range of this data set?
A. 4 — the difference between adjacent scores
B. 7 — Range = X_max − X_min = 9 − 2 = 7 [CORRECT]
C. 5 — the number of scores
D. 9 — the maximum value
Correct Answer: B — B. 7 — Range = X_max − X_min = 9 − 2 = 7
Rationale: The range is the difference between the maximum and minimum scores: Range =
X_max − X_min = 9 − 2 = 7. Option A (4) appears to compute the difference between adjacent
scores, which is not a definition of range. Option C (5) reports the count of scores (n), not the
range. Option D (9) reports only the maximum value without subtracting the minimum. The range is
a single number capturing total spread from lowest to highest.
Q3: Compute the interquartile range (IQR) for the following data set: 2, 4, 6, 8, 10, 12, 14,
16.
A. 8 — Q1 = median of lower half {2,4,6,8} = 5; Q3 = median of upper half {10,12,14,16} =
13; IQR = Q3 − Q1 = 13 − 5 = 8 [CORRECT]
B. 9 — the median of the full data set, confusing IQR with the median
C. 14 — the range (16 − 2), confusing IQR with the range
D. 13 — Q3 alone, forgetting to subtract Q1
Correct Answer: A — A. 8 — Q1 = median of lower half {2,4,6,8} = 5; Q3 = median of
upper half {10,12,14,16} = 13; IQR = Q3 − Q1 = 13 − 5 = 8
Rationale: With n = 8 (even), split the data into a lower half {2,4,6,8} and an upper half
{10,12,14,16}. Q1 = median of the lower half = (4+6)/2 = 5; Q3 = median of the upper half =
(12+14)/2 = 13. Then IQR = Q3 − Q1 = 13 − 5 = 8. Option B (9) reports the median of the full data
set, not the IQR. Option C (14) reports the range (16−2), not the IQR. Option D (13) reports only
Q3, forgetting to subtract Q1. The IQR captures the middle 50% of the data.
Q4: Why is the range considered the most sensitive measure of variability to outliers?
A. Because it uses every score in the data set
B. Because it is based on the mean
C. Because it is computed using the median
D. Because the range is determined solely by the two most extreme scores (X_max and
X_min), so even a single outlier dramatically changes its value [CORRECT]
Correct Answer: D — D. Because the range is determined solely by the two most
extreme scores (X_max and X_min), so even a single outlier dramatically changes its
value
Rationale: The range depends only on the two most extreme scores (the maximum and minimum).
Consequently, a single outlier — either very high or very low — changes one of those two values
and dramatically shifts the range, while leaving the bulk of the data unaffected. Option A is wrong
— the range ignores all interior scores. Option B is wrong — the range does not involve the mean.
Option C is wrong — the range does not involve the median (the IQR does). Because it uses only
two values, the range is highly vulnerable to outliers.
Page 2 | Complete Solution Key
PSYC 354 MODULE 3 QUIZ
Variability | Questions and Answers | 2026 Update | Passed!!
Course PSYC 354 — Statistics for the Behavioral Sciences (Liberty University)
Module 3 Quiz — Variability: Range, IQR, SS, Variance, Standard Deviation &
Assessment
Degrees of Freedom
Total Questions 30 (Multiple Choice, Single Best Answer)
Total Points 100 points (3.33 points per question; Q30 = 3.40 pts)
Cognitive Distribution 30% Recall | 50% Application | 20% Analysis
Format Mix 75% Scenario-Based Calculation & Interpretation | 25% Direct Conceptual
Alignment APA 7th Edition Reporting | 2026–2027 Academic Standards
Range, IQR & Data Spread; SS, Variance & Standard Deviation; Population vs.
Domains Covered Sample Variability, Degrees of Freedom & Behavioral Applications (SPSS/JASP,
MAD, APA 7, AI Screening)
Examiner Directive: This Module 3 examination assesses mastery-level competency in
measures of variability, consistent with the Liberty University PSYC 354 curriculum. Each item
requires absolute mathematical precision, proper statistical notation (σ for population SD, s for
sample SD, σ² and s² for variances, N for population size, n for sample size, SS for sum of
squares, df for degrees of freedom), and foolproof step-by-step rationales. Distractors are
engineered to represent the most common student calculation errors — including dividing by N
instead of n−1 for a sample variance (omitting Bessel's correction), forgetting to square the
deviations in the SS formula, confusing population and sample notation, computing ΣX² instead
of Σ(X−µ)², and mishandling the (ΣX)²/N term in the computational SS formula. The 2026
update integrates contemporary SPSS/JASP variability-table interpretation, robust estimators
such as the Median Absolute Deviation (MAD), modern data visualization (boxplots, violin
plots), AI-assisted outlier screening, and APA 7th-edition reporting standards for variability.
SECTION 1: Fundamentals of Variability — Range, Interquartile
Range, and Data Spread (Q1–Q10)
Q1: Which of the following best defines 'variability' in the context of descriptive
statistics?
A. The central or typical value of a distribution
B. The total number of scores in a data set
C. The degree to which scores in a distribution are spread out or dispersed from each
other and from the central value — providing a quantitative measure of how spread out
the scores are [CORRECT]
D. The probability of obtaining a specific score by chance
Correct Answer: C — C. The degree to which scores in a distribution are spread out or
dispersed from each other and from the central value — providing a quantitative
measure of how spread out the scores are
Page 1 | Complete Solution Key
, PSYC 354 | Statistics for the Behavioral Sciences Module 3 | Variability | 2026 Update
Rationale: Variability (or dispersion) quantifies how spread out or scattered the scores in a
distribution are — how far they deviate from each other and from the central value. Option A
describes central tendency (mean, median, mode), the opposite concept. Option B describes
sample size (N or n). Option D describes probability, not variability. Variability complements central
tendency: together they fully characterize a distribution's shape.
Q2: A clinician records the number of therapy sessions attended by five clients: 3, 7, 4,
9, and 2. What is the range of this data set?
A. 4 — the difference between adjacent scores
B. 7 — Range = X_max − X_min = 9 − 2 = 7 [CORRECT]
C. 5 — the number of scores
D. 9 — the maximum value
Correct Answer: B — B. 7 — Range = X_max − X_min = 9 − 2 = 7
Rationale: The range is the difference between the maximum and minimum scores: Range =
X_max − X_min = 9 − 2 = 7. Option A (4) appears to compute the difference between adjacent
scores, which is not a definition of range. Option C (5) reports the count of scores (n), not the
range. Option D (9) reports only the maximum value without subtracting the minimum. The range is
a single number capturing total spread from lowest to highest.
Q3: Compute the interquartile range (IQR) for the following data set: 2, 4, 6, 8, 10, 12, 14,
16.
A. 8 — Q1 = median of lower half {2,4,6,8} = 5; Q3 = median of upper half {10,12,14,16} =
13; IQR = Q3 − Q1 = 13 − 5 = 8 [CORRECT]
B. 9 — the median of the full data set, confusing IQR with the median
C. 14 — the range (16 − 2), confusing IQR with the range
D. 13 — Q3 alone, forgetting to subtract Q1
Correct Answer: A — A. 8 — Q1 = median of lower half {2,4,6,8} = 5; Q3 = median of
upper half {10,12,14,16} = 13; IQR = Q3 − Q1 = 13 − 5 = 8
Rationale: With n = 8 (even), split the data into a lower half {2,4,6,8} and an upper half
{10,12,14,16}. Q1 = median of the lower half = (4+6)/2 = 5; Q3 = median of the upper half =
(12+14)/2 = 13. Then IQR = Q3 − Q1 = 13 − 5 = 8. Option B (9) reports the median of the full data
set, not the IQR. Option C (14) reports the range (16−2), not the IQR. Option D (13) reports only
Q3, forgetting to subtract Q1. The IQR captures the middle 50% of the data.
Q4: Why is the range considered the most sensitive measure of variability to outliers?
A. Because it uses every score in the data set
B. Because it is based on the mean
C. Because it is computed using the median
D. Because the range is determined solely by the two most extreme scores (X_max and
X_min), so even a single outlier dramatically changes its value [CORRECT]
Correct Answer: D — D. Because the range is determined solely by the two most
extreme scores (X_max and X_min), so even a single outlier dramatically changes its
value
Rationale: The range depends only on the two most extreme scores (the maximum and minimum).
Consequently, a single outlier — either very high or very low — changes one of those two values
and dramatically shifts the range, while leaving the bulk of the data unaffected. Option A is wrong
— the range ignores all interior scores. Option B is wrong — the range does not involve the mean.
Option C is wrong — the range does not involve the median (the IQR does). Because it uses only
two values, the range is highly vulnerable to outliers.
Page 2 | Complete Solution Key
