Statistics for engineers: Which statements about frequency distribution curves are correct?

Introduction / Context:
Understanding shapes of frequency distribution curves helps engineers interpret data from quality control, productivity studies, and risk assessments. Key descriptors include modality, symmetry, and skewness.

Given Data / Assumptions:

• Frequency distributions plotted as smooth curves or histograms.
• Basic statistical terminology: mode, normality, and skewness.
• No numerical calculation is required—only conceptual recognition.

Concept / Approach:
Unimodal distributions show a single mode (peak). A perfectly symmetric, bell-shaped curve is the normal distribution. Asymmetry in the tail (longer tail on one side) indicates skewness—positive (right) or negative (left) skew.

Step-by-Step Solution:
Option A: A single peak implies one mode; unimodal is correct.Option B: Symmetry around the mean defines the normal curve; correct.Option C: Departure from symmetry is skewness; correct.Therefore, all statements are correct and the comprehensive answer is 'all the above.'

Verification / Alternative check:
Plotting sample data (e.g., concrete strength results) often shows near-normal distributions; process shifts can create skewed patterns, validating the definitions.

Why Other Options Are Wrong:

• None of these: Incorrect because each statement is standard statistical terminology.

Common Pitfalls:
Confusing multimodal with skewed; assuming real-world data are perfectly normal—tolerances and processes commonly induce skew.

Final Answer:
all the above.