Can More Readings Reduce Fractional Error in Measurement?

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SUMMARY

Taking multiple readings with vernier calipers, such as measuring the diameter of a coin at (5.06±0.04) mm, does not reduce fractional error caused by systematic errors. Systematic errors are consistent and predictable, allowing for adjustments to be made to obtain the true value. In contrast, random errors are unpredictable and cannot be corrected through averaging. Therefore, averaging multiple readings is ineffective in mitigating systematic errors.

PREREQUISITES
  • Understanding of systematic and random errors in measurements
  • Familiarity with vernier calipers and their usage
  • Knowledge of fractional uncertainty and its calculation
  • Basic principles of statistical averaging
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  • Research methods to identify and correct systematic errors in measurements
  • Learn about the principles of random error analysis
  • Explore advanced techniques for reducing measurement uncertainty
  • Study statistical methods for analyzing measurement data
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Students in physics or engineering, metrology professionals, and anyone involved in precision measurement and error analysis will benefit from this discussion.

Angela Liang
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Why is fractional uncertainty not affected by systematic error? For example à vernier calipers measures the diameter of a coin:
(5.06+-0.04) mm
Can taking more readings, say 6, and taking average, reduce fractional error?
 
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I'm not exactly sure about your terms, but here is my two cents:
A systemic error may be very consistent and predictable. That makes it conceivable to determine the error and make adjustments to the measured value and get the true value. On the other hand, a truly random error is difficult to determine and you can not make adjustments to the measured value.

A systemic error may just repeat the same error over and over, so taking the average of multiple readings will not reduce the error.
 
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FactChecker said:
I'm not exactly sure about your terms, but here is my two cents:
A systemic error may be very consistent and predictable. That makes it conceivable to determine the error and make adjustments to the measured value and get the true value. On the other hand, a truly random error is difficult to determine and you can not make adjustments to the measured value.

A systemic error may just repeat the same error over and over, so taking the average of multiple readings will not reduce the error.
Thanks!
 

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