Calculating uncertainty in data.

In summary, the question concerns finding the uncertainty in the overall average of pendulum data, and the equation for this is \sigmaaverage = \sigma individual/ square root of n. The attempt at a solution involves calculating the uncertainties of individual measurements using the standard deviation or average, and in the case of n approaching infinity, the standard deviation of the mean value approaches 0.
  • #1
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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.
 
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  • #2
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]
 

What is uncertainty in data?

Uncertainty in data refers to the range of possible values that a measurement or calculation could have, due to limitations in the measurement process or inherent variability in the data.

Why is it important to calculate uncertainty in data?

Calculating uncertainty in data is important because it allows us to understand the reliability and accuracy of our results. It helps us to identify potential sources of error and make informed decisions based on the level of uncertainty.

How is uncertainty in data calculated?

Uncertainty in data is typically calculated using statistical methods, such as standard deviation or confidence intervals. These methods take into account the variability and precision of the data to determine the range of possible values.

What are the different types of uncertainty in data?

There are two main types of uncertainty in data: random uncertainty and systematic uncertainty. Random uncertainty is caused by inherent variability in the data, while systematic uncertainty is caused by factors that consistently affect the data.

How can uncertainty be reduced in data?

There are several ways to reduce uncertainty in data, including improving the precision and accuracy of measurements, increasing sample size, and using more reliable equipment or methods. It is also important to identify and address potential sources of systematic uncertainty.

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