List of top Data Adjustment / Least Squares Questions

A trapezoidal land parcel for a residential plot measures 10.335 m in the south, 13.971 m in the north, 5.047 m in the west and 6.302 m in the east directions. The north and south sides are perpendicular to the western side of the plot, making the eastern side skewed. Given the lengths of the sides are measured with a precision of 1 mm, the precision of the area of the plot calculated from these measurements is __________ m² (Rounded off to two decimal values).

Hint: \( \text{Area of a trapezium} = \left(\dfrac{\text{sum of parallel sides}}{2}\right) \times \text{height} \)

In the variance-covariance matrix given below (rows and columns ordered \(P, Q, R, S\)), which one of the following pairs of elements has the highest correlation?
\[ \begin{bmatrix} 0 & 0 & 0 & 0 \\ 0 & 3.73 & 1.85 & 3.23 \\ 0 & 1.85 & 0.93 & 1.61 \\ 0 & 3.23 & 1.61 & 2.79 \end{bmatrix} \]

In the triangulation network shown in the figure, \(b\) and \(g\) are the observed lengths of the baselines, while 1 to 18 are the observed interior angles. The number of redundant observations is __________ (Answer in integer).

The length of a highway was measured in 10 equal sections. If the precision of the individual section measurements is \(\sigma\), then what is the precision of the measured length of the highway?