Using the three routes, what is the adjusted difference in elevation between BM 34 and BM 35, in meters?

• A. 6.185
• B. 6.180
• C. 6.190
• D. 6.175

Answer: (A)

When you have three routes between two benchmarks, each route gives an observed difference in elevation, and each observation has some uncertainty. To get the best single estimate of the true elevation difference, you combine the measurements using a least-squares adjustment, which weights more precise observations more heavily.

If you know the uncertainties (standard deviations) of each route, the adjusted difference is the weighted average: D_adj = (D1/σ1^2 + D2/σ2^2 + D3/σ3^2) / (1/σ1^2 + 1/σ2^2 + 1/σ3^2). If the routes have similar precision, this is close to the simple average (D1 + D2 + D3) / 3. After performing the adjustment, you can look at the residuals to see if any route is inconsistent with the others; large residuals suggest potential errors that may need rechecking.

Using the data from the three routes, the least-squares combination yields 6.185 meters as the best estimate of the adjusted elevation difference between BM 34 and BM 35.