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

To determine the most probable difference in elevation between Benchmark 12 (BM 12) and Benchmark 13 (BM 13) using the weighted value method, the focus lies in understanding how the weighted average is calculated. The weighted value method helps in obtaining a more reliable estimate of differences in elevation by taking into account the precision of different measurements.

When applying this method, measurements that have a higher precision (lower errors) are given more weight, while those with lesser reliability receive less weight. This leads to a calculated difference that more accurately reflects the true elevation change between the two benchmarks.

The process involves computing the elevation differences between the benchmarks using the various measurements taken and then applying the respective weights based on their reliability. The answer of 0.867 suggests that through careful computation and application of the weights according to the reliability of the data drawn from various observations, this value emerges as the best estimate.

The other options represent possible values that could be calculated but do not conform to the calculated weighted average using the actual precision of the observations made between these benchmarks. Hence, the chosen value represents the result of the analytical process typical in geodetic measurements, ensuring that the most accurate representation of the difference is achieved.