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GATE 2024 CE (CE2) – Question 32

Geomatics Engineering · Principles of surveying: plane and geodetic surveying, errors and adjustment · 1 mark · Multiple choice

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 30° 30' 00", 30° 29' 40", 30° 30' 20" and 30° 31' 20". Assuming that each measurement is taken with equal precision, the most probable value of the bearing is

  1. 30° 29' 40"
  2. 30° 30' 20"
  3. 30° 30' 00"
  4. 30° 31' 20"

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Correct answer: (B) 30° 30' 20"

Explanation

For observations of equal precision the most probable value is the arithmetic mean. Taking 30° 30' 00" as the reference, the differences are 0, −20", +20" and +80", with the mean $\frac{80}{4} = +20''$. The most probable bearing is 30° 30' 20".