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ERRORS AND ERROR PROPAGATION
INTRODUCTION:
Laboratory experiments involve taking measurements and using
those measurements in an equation to calculate an experimental result. It is also
necessary to know how to estimate the uncertainty, or error, in physical measurements
and to know how to use those uncertainties to calculate the error in the experimental
result.
TYPES OF EXPERIMENTAL ERRORS
Experimental errors can generally be classified into three types: personal, systematic,
and random.
Personal Errors
These errors arise from personal bias of carelessness in reading an instrument, in
recording data, or in calculations, and parallax in reading a meter. Of these, only parallax
errors can be estimated and used in error propagation. Effort should be made to eliminate
experimental errors.
(When looking at nondigital meter, there is a small distance between the needle and the
scale. As a result, the reading will change as the observer’s eye position changes from
side to side. This apparent change in reading, due to the change in position of the
observer’s eye, is called parallax.)
Systematic Errors
Errors of this type result in measured values which are consistently to high or to low.
Conditions which lead to systematic errors are as follows:
1. An improperly calibrated instrument such as a thermometer which consistently
reads 99ºC in boiling water instead of 100ºC.
2. A meter, micrometer, vernier caliper, or other instrument which was not
properly zeroed or for which the zero correction factor was not considered.
3. Theoretical errors due to a simplified mathematical model for the system
which consistently gives a calculated value different from the calculated value
predicted from a more accurate mathematical model.
Random Errors
Random errors result from unknown and unpredictable variations in experimental
measurements. Possible sources of random errors are:
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1. Observationale.g. , errors when reading the scale of a measuring device to the
smallest division.
2. Environmental unpredictable fluctuations in readings beyond the
experimenters control. Such errors can be determined statistically or can be
estimated by the experimenter.
STATISTICAL DETERMINATION OF RANDOM ERRORS
When there are many measurements of the same quantity, the average or mean value is
defined by
!
=
=
N
i
i
x
N
x
1
_
1
where
i
x
is the
i
th
measured value and
N
is the total number of
measurements.
There are two ways to statistically calculate the uncertainty in the measured value. One
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 Fall '08
 Parsons,B
 Physics, 2 $, 2.00m, 1.00m, 0.1 $, 2.4cm

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