Quick Uncertainty in an Average Question

In summary, when two measurements have the same uncertainty and are equal, the uncertainty of their average is half the original uncertainty.
  • #1
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I took two measurements of angles that have the same uncertainty. These two angles are also equal. So I took an average of these angles and it's the same result originally measured, but when I try finding the UNCERTAINTY OF THE AVERAGE, I get 0. I'm guessing this isn't the right thing to put in my lab report.

So how does it work when you have two exact same measurements with equal errors, how do you get the uncertainty of the average?

Thanks
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  • #2
In general the variance of the average is the average of the variances divided by the number of terms. In your case, since the variances are the same, the variance of the average is half the common variance. The uncertainty (square root of variance) is therefore the original uncertainty divided by the square root of 2.
 
  • #3
response:

Hello there,

Thank you for sharing your experience with uncertainty in an average question. It can definitely be confusing when you have two exact same measurements with equal errors and are trying to calculate the uncertainty of the average.

In this case, it is important to understand that the uncertainty of the average is not simply the average of the uncertainties of the individual measurements. Instead, it is calculated using a formula that takes into account the number of measurements and their individual uncertainties.

Without knowing the specific values and units of your measurements, it is difficult for me to provide a specific answer. However, I would recommend consulting your lab manual or instructor for guidance on how to calculate the uncertainty of the average in your specific case.

In general, the uncertainty of the average can be found by taking the standard deviation of the measurements and dividing it by the square root of the number of measurements. This takes into account the variability of the individual measurements and gives a more accurate representation of the uncertainty in the average.

I hope this helps and good luck with your lab report!

 

1. What is quick uncertainty in an average question?

Quick uncertainty in an average question refers to the margin of error or range of possible values around an average or mean value that is calculated from a sample. It is a measure of the precision or reliability of the average and takes into account the variability of the data.

2. How is quick uncertainty calculated?

Quick uncertainty is calculated using a formula that takes into account the sample size, standard deviation, and confidence level. The formula is: quick uncertainty = (standard deviation / square root of sample size) * critical value, where the critical value is determined by the chosen confidence level.

3. Why is quick uncertainty important in research?

Quick uncertainty is important in research because it allows us to understand the reliability of the average or mean value that is calculated from a sample. It also helps us to determine the confidence we can have in the results and whether they are statistically significant.

4. How can I decrease quick uncertainty in my research?

To decrease quick uncertainty in research, you can increase the sample size, which will reduce the standard deviation and therefore decrease the margin of error. You can also increase the confidence level, which will result in a larger critical value and a smaller margin of error.

5. Is quick uncertainty the same as standard error?

No, quick uncertainty and standard error are not the same. Standard error is a measure of the precision of an estimated population parameter, while quick uncertainty is a measure of the precision of an average or mean value calculated from a sample. However, they are both measures of variability and can be used to calculate confidence intervals.

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