Physics307L F07:Schedule/Week 14 agenda/Weighted
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The problem: You have two separate measurements with different uncertainties. How do you combine them?
Example #1: Brian's Planck's Constant
1st order was found to be (7.23 +/- 0.02) E-34 (J s).
2nd order was found to be (5.94 +/- 0.03) E-34 (J s)
Example #2: Zane's Speed of Light
Derivation
First let's think about what we expect
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]
