A micrometer screw gauge with a resolution of is used to measure the diameter of a…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Quantities, units and the practice of measurement · Uncertainty in measurement

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

Problem

A micrometer screw gauge with a resolution of

0.01\,\mathrm{mm}

is used to measure the diameter of a steel ball bearing six times, giving the readings (mm):

6.02,\ 6.04,\ 6.03,\ 6.05,\ 6.03,\ 6.04

. ((a)) Calculate the mean diameter

\bar x

and the sample standard deviation

s

of the six readings. ((b)) Calculate the standard error of the mean,

\sigma_{\bar x}

. ((c)) If only one reading had been taken, state the bound you would assign to it, using the micrometer's resolution alone.

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