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1
All measurements always have some uncertainty.
We refer to the uncertainty as the error
in the measurement.
Errors fall into two categories:
1.
Systematic Error

errors resulting from measuring devices being out of
calibration.
Such measurements will be consistently too small or too large.
These
errors can be eliminated by precalibrating against a known, trusted standard.
2.
Random Errors

errors resulting in the fluctuation of measurements of the same
quantity about the average.
The measurements are equally probable of being too
large or too small.
These errors generally result from the fineness of scale
division of a measuring device.
Physics is a quantitative science and that means a lot of measurements and calculations.
These calculations involve measurements with uncertainties and thus it is essential for the
physics student to learn how to analyze these uncertainties (errors) in any calculation.
Systematic errors are generally “simple” to analyze but random errors require a more
careful analysis and thus it will be our focus. There is a statistical method for calculating
random uncertainties in measurements.
This requires taking at least 10 measurements of
a quantity.
We will consider such method later on in the lab.
For now we will consider
the uncertainty associated with one single measurement.
The following general rules of thumb are often used to determine the uncertainty in a
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 Fall '09
 Luna

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