The sum of the squared residuals of four measurements of a geodetic baseline is 0.0188. What is the probable error of the baseline?

• A. ± 0.037
• B. ± 0.027
• C. ± 0.032
• D. ± 0.017

Answer: (B)

When you have several measurements of the same baseline, you assess how spread out the results are around their average. The sum of squared residuals, here 0.0188, is a measure of that dispersion among the four readings.

First estimate the standard deviation of the individual measurements: s^2 = SSR/(n−1) = 0.0188/3 = 0.0062667, so s ≈ 0.0792.

The standard error of the mean (the uncertainty of the baseline length you would report as the result) is SE = s/√n = 0.0792/√4 = 0.0792/2 = 0.0396.

The probable error of the baseline length is PE = 0.6745 × SE ≈ 0.6745 × 0.0396 ≈ 0.0267, which rounds to ±0.027.

So the probable error of the baseline is about ±0.027 (in the same units as the measurements).