A report states: "We recorded the running mean diameter of a wire after every…
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Designing and running experiments
Measurement and Method, Ch Running it: troubleshooting, the systematics hunt, safety and the record
Problem
A report states: "We recorded the running mean diameter of a wire after every micrometer reading. By the 30th reading, successive running means differed by less than 0.0003mm, so we judged the mean had converged and stopped." A separate calibration run of many readings on the same micrometer (Chapter 3) gives a sample standard deviation of a single reading s=0.0090mm.
((a)) Show that the expected change in the running mean on adding one more reading, ∣xˉN+1−xˉN∣, is of order s/(N+1), and evaluate it at N=30.
((b)) Explain why the observed flatness at reading 30 is not evidence that enough data had been taken, and state what should have replaced "we continued until it settled."