Data Analysis, Computations, and Mapping
What this domain tests
This domain tests computation discipline: adjustment, coordinate geometry, area, transformations, and map presentation.
Core rules
- Least squares minimizes the sum of squared residuals and yields standard deviations. Check residuals for blunders before rejecting an observation.
- Precision describes repeatability; accuracy describes closeness to truth. A tight standard deviation does not cure a systematic error.
- Area by coordinates uses the shoelace formula; 43,560 ft² = 1 acre. Report area to sensible precision and show the boundary used.
- Transformations need matching datums, epochs, units, and control. A four-parameter transformation is not a substitute for a proper datum transformation.
- Maps should state basis of bearing, datum, scale, north arrow, and whether lines are boundary, occupation, or computed.
Worked example
Four repeated distance measurements are 100.00, 100.02, 99.98, and 100.00 ft. The mean is 100.00 ft. Residuals are 0.00, +0.02, −0.02, and 0.00 ft. The sample standard deviation is √[(0 + 0.0004 + 0.0004 + 0) / 3] = √0.000267 ≈ 0.0163 ft. Reporting “100.000 ft” overstates precision; “100.00 ft ± 0.02 ft” is more honest.
Traps
Averaging coordinates when distances were measured; discarding an inconvenient residual without a blunder analysis; mixing angular and linear residuals; reporting more digits than the data support; and using an unadjusted sketch as a record map.