Mathematics and Statistics Flashcards
6 cards from real FUNDAMENTAL SURVEYING practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 Mathematics and Statistics flashcards as text
What is the most probable value (MPV) in surveying?
Answer: The arithmetic mean of a set of equally weighted observations
The MPV is the arithmetic mean, which minimizes the sum of the squares of the residuals under the method of least squares.
If a traverse has a linear closure of 0.50 ft over a total distance of 2,500 ft, what is the precision ratio?
Answer: 1/5,000
Precision ratio = closure error / total distance = 0.50 / 2,500 = 1/5,000.
What trigonometric formula is used to compute the area of a triangle given two sides and the included angle?
Answer: Area = (1/2) × a × b × sin(C)
The formula Area = (1/2) × a × b × sin(C) uses two sides and the included angle to compute area.
A surveyor measures an angle 6 times and gets a standard deviation of 5″. What is the standard error of the mean?
Answer: 2.04″
Standard error of the mean = σ / √n = 5 / √6 ≈ 2.04″.
What is the departure (ΔE) of a line with a length of 200 ft and a bearing of S 30° W?
Answer: -100.0 ft
Departure = L × sin(bearing angle) × sign = 200 × sin(30°) = 100 ft, negative because it's westward = -100.0 ft.
In least squares adjustment, what quantity is minimized?
Answer: Sum of squared residuals
Least squares adjustment minimizes the sum of the squares of the residuals (v^T P v).