Combining a systematic correction with a random error
A tape 0.012 ft short and thirteen settings of it. The systematic part is removed by arithmetic and the random part is carried as an uncertainty - and the two must never be combined in quadrature, which is the mistake the problem exists to prevent.
Apply· about 20 minutes by hand· 4 steps
Given
A line was taped and recorded as 1247.60 ft. It was laid off in 12 full tape lengths of a nominal 100 ft tape plus a partial length of 47.60 ft - 13 independent settings of the tape in all.
The tape was subsequently standardised and found to be 99.988 ft long under the tension, temperature and support used in the field. It is therefore 0.012 ft short of its nominal 100.00 ft.
The random error of each setting - marking, plumbing and reading - is ±0.006 ft.
All other systematic effects (slope, temperature, tension, sag) have already been corrected out of the recorded 1247.60 ft.
Distances in US survey feet.
Required
The corrected length of the line.
The random uncertainty of the corrected length.
A statement of the result, and a demonstration of why the two quantities do not combine in quadrature.
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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