PSYC 354 | Statistics for the Behavioral Sciences Quiz 2 | Central Tendency | 2026 Update
PSYC 354 QUIZ 2
Central Tendency | Actual Questions and Answers | 2026 Update | 100% Correct
Course PSYC 354 — Statistics for the Behavioral Sciences (Liberty University)
Assessment Quiz 2 — Measures of Central Tendency & Distribution Shapes
Total Questions 30 (Multiple Choice, Single Best Answer)
Total Points 100 points (3.33 points per question)
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
Mean, Median, Mode (Definitions, Calculations, Properties); Skewness, Kurtosis &
Domains Covered Distribution Shapes; Weighted Mean, Data Transformations & Behavioral Science
Applications (SPSS/JASP, Trimmed Means, APA Reporting, AI-Assisted Screening)
Examiner Directive: This examination assesses mathematical rigor and conceptual mastery of
measures of central tendency consistent with the Liberty University PSYC 354 curriculum.
Each item requires absolute precision in calculation, proper statistical notation (M for sample
mean, µ for population mean, ΣX for the sum of scores, X■ for the sample mean symbol when
handwritten), and foolproof, step-by-step mathematical rationales. Distractors are engineered
to represent the most common student calculation errors — including dividing by N−1 instead of
N for a population mean, confusing the direction of skewness, miscalculating the weighted
mean by averaging group means rather than weighting by sample size, and misidentifying the
mode in a bimodal distribution. The 2026 update integrates modern SPSS/JASP
descriptive-statistics output interpretation, robust estimators such as the trimmed mean, and
APA 7th-edition reporting standards for central tendency.
SECTION 1: Mean, Median, Mode — Definitions, Calculations,
and Properties (Q1–Q10)
Q1: A behavioral researcher records the number of anxiety symptoms reported by five
participants: 3, 7, 4, 9, and 2. What is the sample mean (M) for this data set?
A. 4.0 — the median, not the mean
B. 5.0 — ΣX = 3+7+4+9+2 = 25; M = ΣX / n = = 5.0 [CORRECT]
C. 6.25 — dividing ΣX by n−1 = 4 (the sample standard deviation denominator, not the mean)
D. 25.0 — reporting ΣX without dividing by n
Correct Answer: B — B. 5.0 — ΣX = 3+7+4+9+2 = 25; M = ΣX / n = = 5.0
Rationale: The sample mean is computed as M = ΣX / n. Here, ΣX = 3+7+4+9+2 = 25 and n = 5,
so M = = 5.0. Option A (4.0) is the median of the ordered set {2,3,4,7,9}, confusing central
tendency measures. Option C (6.25) incorrectly divides by n−1 = 4, which is the denominator for
the sample variance, not the mean. Option D (25.0) reports the raw sum without averaging. The
mean requires dividing the sum of all scores by the number of scores.
Page 1 | Complete Solution Key
, PSYC 354 | Statistics for the Behavioral Sciences Quiz 2 | Central Tendency | 2026 Update
Q2: A statistician is describing the average of an entire population of depression scores.
Which symbol should be used to denote this population mean, and how does it differ
from the sample mean notation?
A. M — used for both sample and population means
B. µ (mu) — denotes the population mean; M (or X■) denotes the sample mean, and the
distinction preserves inferential-statistics logic [CORRECT]
C. ΣX — denotes the population mean
D. σ — denotes the population mean
Correct Answer: B — B. µ (mu) — denotes the population mean; M (or X■) denotes the
sample mean, and the distinction preserves inferential-statistics logic
Rationale: By convention, Greek letters denote population parameters and Roman (italic) letters
denote sample statistics. The population mean is µ (mu); the sample mean is M or X■. ΣX denotes
the sum of the scores (not the mean itself), and σ denotes the population standard deviation (not
the mean). This notation distinction is foundational to inferential statistics because hypotheses are
typically framed about µ but estimated from M.
Q3: Which of the following is a defining mathematical property of the mean?
A. The mean is always the most frequently occurring score
B. The sum of the deviation scores (X − M) from the mean equals zero: Σ(X − M) = 0
[CORRECT]
C. The mean is unaffected by extreme outliers
D. The mean always equals the middle value when scores are rank-ordered
Correct Answer: B — B. The sum of the deviation scores (X − M) from the mean equals
zero: Σ(X − M) = 0
Rationale: A defining mathematical property of the mean is that the sum of the deviation scores
around it is zero: Σ(X − M) = 0. This is provable algebraically and is the basis for the mean being
the balance point of a distribution. Option A describes the mode. Option C is false — the mean is
the measure of central tendency most sensitive to outliers. Option D describes the median. No
other measure of central tendency satisfies the zero-sum-of-deviations property.
Q4: Find the median of the following data set of reaction times (in ms): 8, 3, 5, 12, 7, 2.
A. 5.0 — taking only the lower of the two middle values
B. 6.0 — ordered set is {2,3,5,7,8,12}; with even n, median = (5+7)/2 = 6.0 [CORRECT]
C. 6.17 — calculating the mean (ΣX/n = 37/6) instead of the median
D. 7.0 — taking only the upper of the two middle values
Correct Answer: B — B. 6.0 — ordered set is {2,3,5,7,8,12}; with even n, median = (5+7)/2
= 6.0
Rationale: First rank-order the data: {2, 3, 5, 7, 8, 12}. With an even number of scores (n = 6), the
median is the arithmetic mean of the two middle scores (the 3rd and 4th values): (5 + 7) / 2 = 6.0.
Option A reports only the lower middle value (5); Option D reports only the upper middle value (7);
both incorrectly apply the odd-n rule. Option C (6.17) computes the mean ΣX/n = 37/6 ≈ 6.17,
confusing the mean with the median. With even n, the median always requires averaging the two
central values.
Q5: What is the mode of the following data set of stress ratings: 4, 2, 7, 4, 9, 4, 2, 7, 7, 1?
A. 4 only — failing to recognize the second most-frequent score
B. 7 only — failing to recognize the most-frequent score
C. 4 and 7 (bimodal) — both scores occur with the highest frequency (3 times each)
[CORRECT]
D. 4.7 — the mean, not the mode
Page 2 | Complete Solution Key
PSYC 354 QUIZ 2
Central Tendency | Actual Questions and Answers | 2026 Update | 100% Correct
Course PSYC 354 — Statistics for the Behavioral Sciences (Liberty University)
Assessment Quiz 2 — Measures of Central Tendency & Distribution Shapes
Total Questions 30 (Multiple Choice, Single Best Answer)
Total Points 100 points (3.33 points per question)
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
Mean, Median, Mode (Definitions, Calculations, Properties); Skewness, Kurtosis &
Domains Covered Distribution Shapes; Weighted Mean, Data Transformations & Behavioral Science
Applications (SPSS/JASP, Trimmed Means, APA Reporting, AI-Assisted Screening)
Examiner Directive: This examination assesses mathematical rigor and conceptual mastery of
measures of central tendency consistent with the Liberty University PSYC 354 curriculum.
Each item requires absolute precision in calculation, proper statistical notation (M for sample
mean, µ for population mean, ΣX for the sum of scores, X■ for the sample mean symbol when
handwritten), and foolproof, step-by-step mathematical rationales. Distractors are engineered
to represent the most common student calculation errors — including dividing by N−1 instead of
N for a population mean, confusing the direction of skewness, miscalculating the weighted
mean by averaging group means rather than weighting by sample size, and misidentifying the
mode in a bimodal distribution. The 2026 update integrates modern SPSS/JASP
descriptive-statistics output interpretation, robust estimators such as the trimmed mean, and
APA 7th-edition reporting standards for central tendency.
SECTION 1: Mean, Median, Mode — Definitions, Calculations,
and Properties (Q1–Q10)
Q1: A behavioral researcher records the number of anxiety symptoms reported by five
participants: 3, 7, 4, 9, and 2. What is the sample mean (M) for this data set?
A. 4.0 — the median, not the mean
B. 5.0 — ΣX = 3+7+4+9+2 = 25; M = ΣX / n = = 5.0 [CORRECT]
C. 6.25 — dividing ΣX by n−1 = 4 (the sample standard deviation denominator, not the mean)
D. 25.0 — reporting ΣX without dividing by n
Correct Answer: B — B. 5.0 — ΣX = 3+7+4+9+2 = 25; M = ΣX / n = = 5.0
Rationale: The sample mean is computed as M = ΣX / n. Here, ΣX = 3+7+4+9+2 = 25 and n = 5,
so M = = 5.0. Option A (4.0) is the median of the ordered set {2,3,4,7,9}, confusing central
tendency measures. Option C (6.25) incorrectly divides by n−1 = 4, which is the denominator for
the sample variance, not the mean. Option D (25.0) reports the raw sum without averaging. The
mean requires dividing the sum of all scores by the number of scores.
Page 1 | Complete Solution Key
, PSYC 354 | Statistics for the Behavioral Sciences Quiz 2 | Central Tendency | 2026 Update
Q2: A statistician is describing the average of an entire population of depression scores.
Which symbol should be used to denote this population mean, and how does it differ
from the sample mean notation?
A. M — used for both sample and population means
B. µ (mu) — denotes the population mean; M (or X■) denotes the sample mean, and the
distinction preserves inferential-statistics logic [CORRECT]
C. ΣX — denotes the population mean
D. σ — denotes the population mean
Correct Answer: B — B. µ (mu) — denotes the population mean; M (or X■) denotes the
sample mean, and the distinction preserves inferential-statistics logic
Rationale: By convention, Greek letters denote population parameters and Roman (italic) letters
denote sample statistics. The population mean is µ (mu); the sample mean is M or X■. ΣX denotes
the sum of the scores (not the mean itself), and σ denotes the population standard deviation (not
the mean). This notation distinction is foundational to inferential statistics because hypotheses are
typically framed about µ but estimated from M.
Q3: Which of the following is a defining mathematical property of the mean?
A. The mean is always the most frequently occurring score
B. The sum of the deviation scores (X − M) from the mean equals zero: Σ(X − M) = 0
[CORRECT]
C. The mean is unaffected by extreme outliers
D. The mean always equals the middle value when scores are rank-ordered
Correct Answer: B — B. The sum of the deviation scores (X − M) from the mean equals
zero: Σ(X − M) = 0
Rationale: A defining mathematical property of the mean is that the sum of the deviation scores
around it is zero: Σ(X − M) = 0. This is provable algebraically and is the basis for the mean being
the balance point of a distribution. Option A describes the mode. Option C is false — the mean is
the measure of central tendency most sensitive to outliers. Option D describes the median. No
other measure of central tendency satisfies the zero-sum-of-deviations property.
Q4: Find the median of the following data set of reaction times (in ms): 8, 3, 5, 12, 7, 2.
A. 5.0 — taking only the lower of the two middle values
B. 6.0 — ordered set is {2,3,5,7,8,12}; with even n, median = (5+7)/2 = 6.0 [CORRECT]
C. 6.17 — calculating the mean (ΣX/n = 37/6) instead of the median
D. 7.0 — taking only the upper of the two middle values
Correct Answer: B — B. 6.0 — ordered set is {2,3,5,7,8,12}; with even n, median = (5+7)/2
= 6.0
Rationale: First rank-order the data: {2, 3, 5, 7, 8, 12}. With an even number of scores (n = 6), the
median is the arithmetic mean of the two middle scores (the 3rd and 4th values): (5 + 7) / 2 = 6.0.
Option A reports only the lower middle value (5); Option D reports only the upper middle value (7);
both incorrectly apply the odd-n rule. Option C (6.17) computes the mean ΣX/n = 37/6 ≈ 6.17,
confusing the mean with the median. With even n, the median always requires averaging the two
central values.
Q5: What is the mode of the following data set of stress ratings: 4, 2, 7, 4, 9, 4, 2, 7, 7, 1?
A. 4 only — failing to recognize the second most-frequent score
B. 7 only — failing to recognize the most-frequent score
C. 4 and 7 (bimodal) — both scores occur with the highest frequency (3 times each)
[CORRECT]
D. 4.7 — the mean, not the mode
Page 2 | Complete Solution Key
