GATE 2021 CE (CE2) – Question 35

Geomatics Engineering · Principles of surveying: plane and geodetic surveying, errors and adjustment · 1 mark · Numerical answer

Surveyors report an angle as 36°30′,36°00′,35°30′,36°30′ based on 4,3,8,4 observations respectively. Find its most probable value in degrees to two decimals.

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Correct answer: 36 to 36

Explanation

For equal precision per observation, weight each reported mean by its number of observations. The weighted mean is $[4(36.5)+3(36)+8(35.5)+4(36.5)]/(4+3+8+4)=684/19=\mathbf{36.00^\circ}$. Minutes must first be converted to decimal degrees.