Quality control statistics: If the average compressive strength of specimens is 4000 kg/cm2 with a standard deviation of 500, what is the coefficient of variation (COV) expressed as a percentage?

Introduction / Context:
The coefficient of variation (COV) is a normalized measure of dispersion used to compare variability across mixes, plants, or time periods. It helps assess process control and the reliability of characteristic strengths.

Given Data / Assumptions:

• Mean (average) strength = 4000 kg/cm2.
• Standard deviation (sd) = 500 kg/cm2.
• COV = (sd / mean) * 100%.

Concept / Approach:
COV expresses scatter relative to the mean, enabling apples-to-apples comparison independent of absolute strength level. Lower COV indicates better process control and more uniform concrete quality.

Step-by-Step Solution:
Compute ratio: sd / mean = 500 / 4000 = 0.125.Convert to percentage: 0.125 * 100 = 12.5%.Select 12.5%.

Verification / Alternative check:
Sanity check: a COV of 12.5% is moderate; many plants target below about 10% for well-controlled mixes.

Why Other Options Are Wrong:
10% underestimates; 15–20% overestimate for the given numbers.

Common Pitfalls:
Forgetting to multiply by 100; mixing up units; using characteristic instead of mean in the denominator.

Final Answer:
12.5%.