A laser distance sensor is used to measure the depth of a puddle repeatedly

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Repeated readings: scatter, the mean and the standard error

Problem

A laser distance sensor is used to measure the depth of a puddle repeatedly. From

N=10

readings the sample standard deviation is

s = 0.20\,\mathrm{mm}

. The sensor's specification gives a bound of

\pm0.05\,\mathrm{mm}

from effects that repeated readings cannot remove. ((a)) Someone argues: "More readings make the measurement more precise, so with

N=40

readings the sample standard deviation will fall to about

0.05\,\mathrm{mm}

." Explain what is wrong with this, and state what actually happens to

s

N

increases. ((b)) Calculate the standard error of the mean at

N=40

. ((c)) Using the rule that readings are worth taking until the standard error is about a third of the largest effect repetition cannot remove, estimate how many readings are worth taking.

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