Understanding Error Propagation in Averaging Measurements

In summary, the conversation discusses calculating the average and error of three measurements. The speaker is confused about why the error value for the average is much higher than the individual errors. The summary also mentions a suggested solution of dividing the sum under the root by three for the arithmetic mean.
  • #1
davidp92
12
0
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+...)
 
Mathematics news on Phys.org
  • #2
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.
 

What is error propagation and why is it important in scientific research?

Error propagation is the process of determining how uncertainties or errors in measurements or calculations affect the overall uncertainty of a result. It is important in scientific research because it allows for a better understanding of the reliability and accuracy of experimental data and findings.

How do you calculate error propagation?

Error propagation can be calculated using the uncertainty or error of each individual measurement or calculation, and then combining these values using mathematical rules to determine the overall uncertainty of the final result. This can be done using methods such as the sum or difference rule, product or quotient rule, or the power rule.

What factors can contribute to error propagation?

There are several factors that can contribute to error propagation, including instrument limitations, human error, systematic errors, and random errors. These errors can be caused by a variety of factors such as improper calibration, faulty equipment, or incorrect data recording.

How can error propagation be minimized?

Error propagation can be minimized by using precise and accurate measurement tools, properly calibrating instruments, and ensuring careful and accurate data recording. It is also important to identify and account for any potential sources of error in the experimental design and data analysis.

Can error propagation ever be completely eliminated?

No, error propagation cannot be completely eliminated as there will always be some level of uncertainty in measurements and calculations. However, by following proper procedures and taking necessary precautions, the impact of error propagation can be minimized and the accuracy of results can be improved.

Similar threads

I Formula for the propagation of complex errors
    • General Math
Replies
5
Views
1K
I Error Propagation in Measurements
    • General Math
Replies
3
Views
1K
I Calculating Collection Rate Error in Labs
    • General Math
Replies
31
Views
1K
Error propagation leads to different uncertainties, which do I choose?
    • Introductory Physics Homework Help
Replies
15
Views
1K
I Error propagation and symmetric errors
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
I How to propagate errors through a regression & non-linear model?
    • General Math
Replies
8
Views
2K
Why is the error value higher in the average calculation?
    • Introductory Physics Homework Help
Replies
1
Views
1K
I Error propagation of a variable for an integral
    • General Math
Replies
6
Views
3K
I Propagation of Errors, Ohm's Law
    • Classical Physics
Replies
6
Views
2K
Error propagation when using modulus operator
    • General Math
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top