Calculating Uncertainty in Averages: A Guide for Scientists

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    Uncertainty
In summary, the conversation is about the Franck-Hertz experiment with heated mercury and electron beams. The speaker has taken data and needs help finding the average difference between each minimum point. They have the locations of the minimums and their uncertainties, but they are unsure how to calculate the uncertainty for their calculations. Two possible methods for calculating the uncertainty are mentioned, the "sum of squares" rule and the "maximal deviations" estimate.
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spikethekitty
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Homework Statement


In my lab we are doing Franck Hurtz experiment with heated mercury and electron beams. We already took data but i need a little help. I have the locations of the minimums A B C D and E, and each point has it's own uncertainty. a b c d and e. What i needed to find was the difference between each min and the next, so A-B, B-C... and then find the average of each these differences. I don't know how to do the uncertainty for my calculations.


Homework Equations


My actual values are
1.4
1.94
2.43
2.98
3.66
With uncertanities (in order)
0.003686
0.008077
0.002263
0.009459
0.003834


The Attempt at a Solution

 
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  • #2
I would say that the most general rule is the "sum of squares" rule,
[tex](\Delta d)^2 = (\Delta x)^2 + (\Delta y)^2[/tex]
where d = x - y is the difference of two independent quantities x and y.

However, I think that
[tex](\Delta d) = (\Delta x) + (\Delta y)[/tex]
is also commonly used, giving the "rough" estimate that the deviation from the mean is at most the sum of the two maximal deviations.
 

1. What is uncertainty?

Uncertainty is the lack of complete knowledge or precision about a certain measurement or value. It is the range of possible values that a measurement or value could potentially have.

2. How is uncertainty calculated?

Uncertainty is typically calculated by analyzing the sources of error or variability in a measurement or value and determining the range of values that could potentially occur.

3. What is the significance of uncertainty in scientific research?

Uncertainty is an important aspect of scientific research because it allows for a more accurate and honest representation of data. It also allows for the evaluation of the reliability and validity of experimental results.

4. How is uncertainty related to averages?

Averages are often used to reduce uncertainty, as they represent a middle ground between all the possible values that could occur. However, the uncertainty of an average depends on the uncertainty of the individual data points used to calculate it.

5. How can uncertainty be reduced?

Uncertainty can be reduced by increasing the precision and accuracy of measurements, controlling for sources of error and variability, and using statistical methods to analyze and interpret data. It is important to also acknowledge and report the level of uncertainty present in research findings.

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