A group measures the terminal velocity of a small steel ball falling through…
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Data analysis and model fitting in the laboratory
Measurement and Method, Ch Do two results agree? Comparison, consistency and outliers
Problem
A group measures the terminal velocity of a small steel ball falling through glycerine by timing its fall over a fixed marked distance, repeating the drop N=12 times with the same ball and the same stopwatch. The 12 readings have sample mean 15.42mms−1 and sample standard deviation 0.48mms−1. One reading, 14.20mms−1, is markedly low; the record of readings notes that a small air bubble was seen clinging to the ball during that drop and was removed before the next run. With that one reading removed, the remaining N=11 readings have sample mean 15.53mms−1 and sample standard deviation 0.30mms−1.
((a)) Suppose the record of readings were silent about the bubble. Apply Chauvenet's criterion to the suspect reading, using the two-sided tail table (z=2.5,3.0,3.5 give P=0.0124,0.0027,4.7×10−4), to say whether the reading is a statistical outlier in the original run of twelve.
((b)) Now use the recorded note. Decide whether it justifies excluding the reading, and write the documented exclusion sentence that should accompany the calculation.
((c)) Report the terminal velocity, with its standard uncertainty, both including and excluding the suspect reading.