Quick Uncertainty in an Average Question

  • Context: Undergrad 
  • Thread starter Thread starter peppies
  • Start date Start date
  • Tags Tags
    Average Uncertainty
Click For Summary
SUMMARY

The discussion centers on calculating the uncertainty of an average when two identical measurements with equal uncertainties are involved. The key conclusion is that the variance of the average is derived from the average of the variances divided by the number of measurements. In this specific case, since both measurements have the same variance, the variance of the average is half of that common variance. Consequently, the uncertainty of the average is the original uncertainty divided by the square root of 2.

PREREQUISITES
  • Understanding of basic statistical concepts such as variance and uncertainty
  • Familiarity with error propagation techniques in measurements
  • Knowledge of averaging methods in experimental data analysis
  • Basic proficiency in mathematical operations involving square roots
NEXT STEPS
  • Research "Error Propagation in Measurements" to understand how uncertainties affect results
  • Study "Variance and Standard Deviation Calculations" for deeper insights into statistical analysis
  • Learn about "Averaging Techniques in Experimental Physics" for practical applications
  • Explore "Statistical Methods for Data Analysis" to enhance data interpretation skills
USEFUL FOR

Students in physics or engineering, researchers conducting experiments, and anyone involved in data analysis requiring precise uncertainty calculations.

peppies
Messages
15
Reaction score
1
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
Best
 
Physics news on Phys.org
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.
 

Similar threads

Undergrad Measurements and uncertainty principle
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Uncertainty Principle in QFT & Early Universe Conditions
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Understanding the meaning of "uncertainty" in Heisenberg's UP
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Time of flight measurement uncertainty
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Double slit experiment and the Uncertainty Principle
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad The Wavefunction when Mass is Much Greater than Planck's Constant
  • · Replies 21 ·
Replies
21
Views
2K
Graduate Is there an uncertainty in energy measurement in quantum mechanics?
  • · Replies 17 ·
Replies
17
Views
3K
Undergrad Does the wave function spread more quickly after it is observed?
  • · Replies 32 ·
2
Replies
32
Views
4K
Undergrad Making sure about the spreads in the Uncertainty Principle
  • · Replies 6 ·
Replies
6
Views
1K
High School Measuring a circle and the Uncertainty principle
  • · Replies 4 ·
Replies
4
Views
9K