Physics307L:Schedule/Week 9 agenda/Weighted
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The problem: You have two separate measurements with different uncertainties. How do you combine them?
Example: Speed of Light
Measurement #1 (25 +/- 3) cm / ns
Measurement #2 29(2) cm / ns
What is the best way to combine these measurements?
What do you expect the new means, uncertainties to be?
Derivation
The formula
Wikipedia article
- [math]\displaystyle{ \bar{x} = \frac{ \sum_{i=1}^n w_i x_i}{\sum_{i=1}^n w_i}, }[/math]
which means:
- [math]\displaystyle{ \bar{x} = \frac{w_1 x_1 + w_2 x_2 + \cdots + w_n x_n}{w_1 + w_2 + \cdots + w_n}. }[/math]
- [math]\displaystyle{ w_i = \frac{1}{\sigma_i^2}. }[/math]
