# Physics307L:Schedule/Week 9 agenda/Weighted

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(Redirected from Physics307L:Schedule/Week 14 agenda/Weighted)

## 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

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \bar{x} = \frac{ \sum_{i=1}^n w_i x_i}{\sum_{i=1}^n w_i}, }**

which means:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \bar{x} = \frac{w_1 x_1 + w_2 x_2 + \cdots + w_n x_n}{w_1 + w_2 + \cdots + w_n}. }**

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle w_i = \frac{1}{\sigma_i^2}. }**