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education/statistics/Measurement Error.md
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@ -8,12 +8,16 @@ Chance errors *change from measurement to measurement but average out over time*
- Chance error is how much an individual measurement varies from the exact value. It can be positive or negative. - Chance error is how much an individual measurement varies from the exact value. It can be positive or negative.
- The standard deviation of repeated measurements gives us the expected size of a chance error - The standard deviation of repeated measurements gives us the expected size of a chance error
```
individual measurement = exact value + chance error
```
$$ IndividualMeasurement = ExactValue + ChanceError $$
# Outliers
Histograms of repeated measurements tend to follow the normal curve.
According to the empirical rule, 99.7% of such measurements should be within 3σ of the exact value.
$$ $
# Terminology # Terminology
| Term | Definition | | Term | Definition |
| -- | -- | | -- | -- |
| Best Guess | Average/Mean | | Best Guess | Average/Mean |
| Off by how much | standard deviation | | Off by how much/Give or take | standard deviation |