Understanding Error Propagation in Averaging Measurements

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SUMMARY

The discussion centers on calculating the average of three measurements and the associated error propagation. The measurements provided are replicate 1 = 8.9 (+/-) 0.71 mg, replicate 2 = 9.3 (+/-) 0.69 mg, and replicate 3 = 8.8 (+/-) 0.70 mg. The correct average is 8.9333 (+/-) e, where e is derived from the square root of the sum of the squares of individual errors. To accurately calculate the error of the average, the total error should be divided by the number of measurements, which is three, rather than simply summing the errors.

PREREQUISITES
  • Understanding of basic statistics, particularly averaging and error propagation.
  • Familiarity with the concept of standard deviation and its application in measurement errors.
  • Knowledge of the formula for error propagation: e=sqrt((e1)^2+(e2)^2+...).
  • Ability to perform arithmetic operations involving fractions and square roots.
NEXT STEPS
  • Study the derivation of the error propagation formula in detail.
  • Learn about the differences between absolute and relative error calculations.
  • Explore the concept of weighted averages and their application in error analysis.
  • Investigate statistical software tools for error analysis, such as R or Python's SciPy library.
USEFUL FOR

Researchers, statisticians, and anyone involved in experimental measurements and data analysis who needs to understand error propagation in averaging measurements.

davidp92
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Not sure if this is the right section to post this..
I have 3 measurements and was trying to take the average of the measurements and calculate the error of the average:
replicate 1 = 8.9 (+/-) 0.71mg
replicate 2 = 9.3 (+/-) 0.69mg
replicate 3 = 8.8 (+/-) 0.70mg

I get an average of 8.9333 (+/-) e where e=sqrt((rep 1 error)^2 + (rep 2 error)^2 + (rep 3 error)^2) which gives me a value of 1.21. But why is the error value so much higher in the average?
What step am I missing? I don't know the derivation behind the error propagation formula - so I just use it as it is: e=sqrt((e1)^2+(e2)^2+...)
 
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If you take the arithmetic mean, then you should divide the sum under the root by three, otherwise you add up errors, which aren't additive. Another measure would be the arithmetic mean of the percentages.
 

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