Two students measured the length of the same rod and reported the results 135 ± 3 mm and 137 ± 3 mm. What is the discrepancy between the two measurements, and is it significant?

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BlackTom AI · Accepted Answer

To tackle this question, I’ll break down what the numbers mean and compare the two measurements carefully.
Option A: '136 mm (significant)'. This choice implies that the two measurements differ by a value that is statistically meaningful and beyond the uncertainty. However, the reported measurements each have an uncertainty of ±3 mm, so a 136 mm central value is not directly relevant here; more importantly, the actual difference between 135 and 137 is 2 mm, which is smaller than the stated uncertainties. Therefore, labeling the discrepancy as significant is not justified.
Option B: '136 mm (not significant)'. Here the central value 136 mm would be a derived estimate, but the problem asks for the discrepancy between the two measurements, not a single combined value. The key question is about the difference (2 mm) and whether that difference is significant given the uncertainties. This option also shifts focus away from the actual difference, making it an incorrect framing.
Option C: '2 mm (significant)'. The raw difference between the two measurements is 2 mm (137 − 135 = 2). Yet, each measurement carries an uncertainty of ±3 mm. When comparing two measurements with uncertainties, we consider whether the difference exceeds the combined uncertainty. The combined standard uncertainty is roughly sqrt(3^2 + 3^2) ≈ 4.24 mm, or, conservatively, if you treat them as independent maximum-errors, the difference of 2 mm is well within the total uncertainty. In practical terms, 2 mm is not statistically significant given ±3 mm uncertainties, so this option is not correct.
Option D: '2 mm (not significant)'. This option correctly states the difference (2 mm) and correctly characterizes its significance relative to the given uncertainties. Since each measurement can vary by up to 3 mm, the observed 2 mm discrepancy lies within the expected range of variation, so it is not significant. This aligns with standard thinking about measurement uncertainty and discrepancy interpretation.
In summary, the correct interpretation is that the two readings differ by 2 mm, but that difference is not significant because it falls within the measurement uncertainties of ±3 mm for each measurement. The remaining options either misstate the discrepancy, misinterpret what is being compared (central value vs. difference), or wrongly assign significance to the difference based on the given uncertainties.

SPHY001 LAB 6 (Pre-Lab) How to Write the Conclusion of a Laboratory Report | LA010

Two students measured the length of the same rod and reported the results 135 ± 3 mm and 137 ± 3 mm. What is the discrepancy between the two measurements, and is it significant?

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