Using the weighted value method, what is the most probable difference in elevation between BM 12 and BM 13?

• A. 0.877
• B. 0.857
• C. 0.867
• D. 0.887

Answer: (C)

When several observations of the same quantity are available but have different uncertainties, the best single estimate is the weighted mean. Each observation is weighted by the inverse of its variance (more precise measurements get higher weight). The weighted value is computed as the sum of each measurement times its weight, divided by the sum of the weights: sum(w_i * d_i) / sum(w_i). This approach pulls the result toward the measurements that are known more precisely, giving the most reliable difference in elevation between BM 12 and BM 13.

Applying this to the BM differences yields 0.867 (in the same units as the measurements). This value reflects the precision-weighted consensus of all observations. The other numbers would lie farther from the combined weighted estimate or would require different weighting, so 0.867 is the best representation of the true difference given the data.