FUNDAMENTAL SURVEYING Mathematics and Statistics 2

Question 1

What is the most probable value (MPV) in surveying?

Accepted Answer

The arithmetic mean of a set of equally weighted observations

Answer

The MPV is the arithmetic mean, which minimizes the sum of the squares of the residuals under the method of least squares.

Question 2

If a traverse has a linear closure of 0.50 ft over a total distance of 2,500 ft, what is the precision ratio?

Accepted Answer

1/5,000

Answer

Precision ratio = closure error / total distance = 0.50 / 2,500 = 1/5,000.

Question 3

What trigonometric formula is used to compute the area of a triangle given two sides and the included angle?

Accepted Answer

Area = (1/2) × a × b × sin(C)

Answer

The formula Area = (1/2) × a × b × sin(C) uses two sides and the included angle to compute area.

Question 4

A surveyor measures an angle 6 times and gets a standard deviation of 5″. What is the standard error of the mean?

Accepted Answer

2.04″

Answer

Standard error of the mean = σ / √n = 5 / √6 ≈ 2.04″.

Question 5

What is the departure (ΔE) of a line with a length of 200 ft and a bearing of S 30° W?

Accepted Answer

-100.0 ft

Answer

Departure = L × sin(bearing angle) × sign = 200 × sin(30°) = 100 ft, negative because it's westward = -100.0 ft.

FUNDAMENTAL SURVEYING Practice Test