1. Random Error Propagation

2. Errors in Indirect Quantities
Thus far, we have worked with errors in direct measurements
Often, we compute other quantities based on our direct measurements (e.g. angles and distances for traverse coordinates)
By the method of error propagation, we can assess the impact of the measurements on the computed quantities

3. Rectangle Example
Area of 100x40 rectangle is A one unit error gives an area of 101x41=4141. The error in area is 141, which is approximately 100x1 + 40x1.

4. Error Propagation Derivation

5. Cut to the Chase or
Note the variance and covariance terms

6. In Matrix Form
The covariance term shows the interdependence between unknowns. (Covariance matrix is symmetric)

7. General Matrix Form

8. For Independent Observations

9. SLOPOV For Nonlinear Functions

12. Example – Cylindrical Tank

15. Horizontal Distance Example