Benchmark carried on two routes and reconciled by weighted mean
A new benchmark is levelled from two published control points over routes of different length. Test the discrepancy, weight each route inversely with its length, and compute the weighted mean elevation and its standard deviation.
Apply· about 18 minutes by hand· 6 steps
Given
A new benchmark BM-C is established and levelled independently from two published control points. Elevations in US survey feet, carried to 0.001 ft.
Route 1, from BM-A: length 3.2 miles, giving BM-C = 1,214.372 ft.
Route 2, from BM-B: length 5.6 miles, giving BM-C = 1,214.418 ft.
The two published control points are themselves held fixed and are assumed error free for this computation.
Tolerance coefficient for this order of work is C = 0.05 ft with the length in miles.
Required
Whether the discrepancy between the two routes is acceptable.
The weight of each route and the weighted mean elevation of BM-C.
An estimate of the precision of the adopted elevation.
Work it through yourself before reading on - the solution below shows every step, so there is no way to skim it without giving the answer away.
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