A digital multimeter with a display resolution of and a manufacturer's specification…

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 digital multimeter with a display resolution of

1\,\mathrm{mV}

and a manufacturer's specification of

\pm(0.5\%\text{ of reading} + 1\text{ digit})

is used to read the steady voltage across a resistor six times, giving (V):

3.212,\ 3.215,\ 3.211,\ 3.214,\ 3.213,\ 3.212

. ((a)) Calculate the mean voltage

\bar V

and the sample standard deviation

s

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

\sigma_{\bar V}

. ((c)) Calculate the bound you would assign to a single one of these readings from the multimeter's specification (take the reading as

3.213\,\mathrm{V}

), and compare it with

\sigma_{\bar V}

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