random and systematic errors[1]
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STAGE 2 PHYSICS TEACHING AND LEARNING STRATEGIES
RANDOM and SYSTEMATIC ERRORS
The following notes have been developed to aid with the teaching of the following Key Idea.
KEY IDEA
Experiments may involve random and/or systematic errors (or uncertainties).
Intended Student Learning
For example, identify sources of random and/or systematic errors in an experiment..
ncertainty in the final result may arise from two types of error! systemati err!r and rand!m
err!r.
Systemati err!rs may be introduced by the experimental conditions" e.g. temperature fluctuations" or
by faulty instruments" e.g. calibration errors. The very presence of the measuring instrument may
change the phenomenon being investigated. #uch errors exist throughout the experiment and hence
cannot be diminished by any statistical averaging process. $ well%designed experiment will minimise
such errors. &here this is not possible" the errors should be investigated and the necessary corrections
made in the 'uantities being measured. It is not possible to give detailed advice as to how systematic
errors may be overcome. Each experiment must be considered individually and only by a thorough
understanding of the obective of the experiment and the techni'ues being used is this possible.
$pparatus fre'uently used in schools include thermometers" balances" stopwatches" micrometer screw
gauges" multimeters and oscilloscopes. $ny measuring device which has not been calibrated is a
liely source of a systematic error.
Rand!m err!rs occur in all measurements. #uppose that an experimenter" taing all possible
precautions against nown errors" were to tae a measurement ten times. *e or she could expect to
obtain results that differ slightly. +or example" a set of ten measurements of the time for a cylinder to
roll down an incline was" in seconds! ,-" ,0" ,-" ,-0" ,-1" 234" ,-0" ,-" ,-3" ,-4. $ssuming
that e'ual care had been taen over each measurement" the most accurate value is the arithmetic mean
(the common average). In this case" the arithmetic mean is ,-5.4 seconds (obtained by adding the
values and dividing by the number of values added). This would be recorded as ,-5 seconds since an
average cannot have more significant figures than the data used to determine the average. 6uoting the
arithmetic mean by itself is insufficient" however" since although it is the most probable value is not
necessarily the true value. &e need an estimate of the amount by which the mean may be in error.
There is a variety of ways of maing this statement about precision of the data. #ome accepted ways
are the range" the mean deviation" or the standard deviation" none of which is re'uired for this
curriculum statement.
A"n!#$edgement
Prepared by the Subject Advisory Committee. Copyright SSABSA
SSABSA Support Materials: 285591429.doc, last updated 8 March 2011 page 1