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Calculating uncertainty in data.

  • Thread starter Encarta
  • Start date
  • #1
17
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Homework Statement


This is from a laboratory exercise. I was asked to measure the time it took for a pendulum to cover 3 periods. I repeated this 25 times, to get 25 measurements for as many trials. I also calculated the standard deviation from the measured data (calculated for different question).

The question I am stuck on, is however, the one that concerns finding the uncertainty in the overall average of the pendulum data. Any help is appreciated.


Homework Equations



I am given this equation for finding the average uncertainty.

[tex]\sigma[/tex]average = [tex]\sigma[/tex] individual/ square root of n
n being number of trials.


The Attempt at a Solution



So, the equations asks for the uncertainties of individual measurements. Can I somehow calculate the individual uncertainties from the standard deviation or the average?

Thanks a lot.
 

Answers and Replies

  • #2
10
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What you are looking for seems to be the variance of measurements.
For the std-deviation of the mean value:
[tex]s_{m}=\frac{s}{\sqrt{n}}=\sqrt{\frac{1}{n(n-1)}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}}[/tex]

here then holds for n->infinity

[tex]s_{m}\rightarrow0\; s\rightarrow\sigma[/tex]

with

[tex]s^{2}=\frac{1}{n-1}\sum(x_{i}-\bar{x})^{2}[/tex]
 

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