random and systematic errors[1]

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7/18/2019 Random and Systematic Errors[1] http://slidepdf.com/reader/full/random-and-systematic-errors1 1/1 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

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Random and Systematic Errors[1]

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Page 1: Random and Systematic Errors[1]

7/18/2019 Random and Systematic Errors[1]

http://slidepdf.com/reader/full/random-and-systematic-errors1 1/1

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