Repeated measurements of the same reference area give 1,999 to 2,001 square feet, while the independently verified reference area is 1,800 square feet. What distinction does this illustrate?
Correct Answer
A) High repeatability can coexist with systematic measurement error
Repeated measurements tightly clustered near 2,000 square feet show repeatability. The verified 1,800 square-foot reference reveals a systematic discrepancy, so repeatability alone does not establish accuracy. Repeatedly reproducing an error does not make it correct. This distinction does not identify which device or calibration defect caused the error without further investigation.
Why This Is the Correct Answer
Option A is correct because the measurements cluster tightly between 1,999 and 2,001 square feet, showing high repeatability, while the verified 1,800 square-foot reference reveals a systematic discrepancy. Repeatability means repeated measurements yield nearly the same value, but that does not establish accuracy. Reproducing an error consistently does not make it correct.
Why the Other Options Are Wrong
Option B: Close repetition proves the measured area is accurate
Option B claims close repetition proves the measured area is accurate, but the readings near 2,000 square feet are about 200 square feet off the verified 1,800. Repeatability does not establish accuracy.
Option C: An error is impossible when the observations cluster tightly
Option C says an error is impossible when observations cluster tightly, which the facts contradict. The tight cluster near 2,000 square feet is consistently wrong compared with the verified 1,800 square feet.
Option D: More repetitions eliminate a systematic discrepancy
Option D says more repetitions eliminate a systematic discrepancy, but repeating a biased method reproduces the same bias. Identifying and correcting the source of the error is required.
Tight group, wrong target
Picture arrows tightly grouped but far from the bullseye: precise, yet not accurate.
How to use: Use this when a question contrasts consistent measurements with a known true value.
Exam Tip
When repeated values agree with each other but not with a verified reference, the answer involves precision without accuracy.
Common Mistakes to Avoid
- -Treating consistent measurements as proof of accuracy
- -Believing more repetitions will remove a systematic error
- -Assuming the cause of the bias is known without investigation
Concept Deep Dive
Analysis
This question tests the difference between precision (repeatability) and accuracy. Measurements clustered tightly near 2,000 square feet are repeatable, but the verified area is 1,800 square feet, revealing a systematic error. The reasoning is that consistency alone does not prove correctness.
Background Knowledge
Precision describes how closely repeated measurements agree with one another, while accuracy describes how close they are to the true value. A method can be precise but inaccurate if it has a systematic bias, such as a miscalibrated device or a consistent measuring convention error. Comparing to a verified reference reveals such bias.
Real-World Application
An appraiser's laser measuring device repeatedly reports about 2,000 square feet for a house whose verified plans and a separate measurement show 1,800 square feet. The appraiser investigates the device and the measuring procedure rather than trusting the consistent readings.
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