GATE CE 2024 Set 2 — Question 32
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Geomatics Engineering → Errors & Adjustment → Theory of Errors
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Question
To finalize the direction of a survey, four surveyors set up a theodolite at a station P and performed all the temporary adjustments. From the station P, each of the surveyors observed the bearing to a tower located at station Q with the same instrument without shifting it. The bearings observed by the surveyors are , , and . Assuming that each measurement is taken with equal precision, the most probable value of the bearing is
Correct answer
(B) 30^o 30' 20''
Solution
For measurements taken with equal precision, the most probable value (MPV) is the arithmetic mean of the observed values.Observed bearings:
Sum =
Since and :
Sum = Arithmetic Mean =
MPV = .
1.
2.
3.
4.
Sum of bearings = Sum =
Since and :
Sum = Arithmetic Mean =
MPV = .
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