Self Study: Random Errors
State results to the accuracy level specified; if not specified, state to an accuracy based on the problem.
Problem (1)
Survey Crew A measured a distance multiple times: 118.54', 118.52', 118.48', 118.54', 118.53', 118.47'.
Determine
The most probable line length
Its standard deviation
The length's expected error
Compute all to 0.001'.
Problem (2)
Two crews measured different distances multiple times. There results, in feet, are shown in the table below:

Crew A
Crew B
Num of meas
4
12
Average
87.96
108.53
Standard deviation
±0.030
±0.035
Which Crew had better:
Precision?
Expected accuracy?
Explain why in both cases and support mathematically.
Problem (3)
The zenith angle to the top of a flag pole was measured with these results: 37°18'55", 37°19'04", 37°19'09", 37°18'53", 37°19'02"
Determine
The most probable zenith angle
Its standard deviation
The angle's expected error
Compute all to 0.1".
Problem (4)
The length and width of a building are measured in feet, summarized in the table below.

Length
Width
173.9
89.6
174.5
90.1
174.3
89.7
What are the building's area and expected area error in square yards?
Problem (5)
A lab technician was to determine the moisture content of a soil sample. She weighed the sample 4 times and obtained an average of 583.4 gr with a ±0.9 gr standard deviation. After the sample was dried for 24 hours at 400° F, she weighed it 6 times for an average of 552.9 gr and standard deviation of ±1.5 gr. What was the soil’s moisture content, and its expected error, in grams?
Problem (6)
Four different survey crews independently measured the elevation difference from point A to B. Because the have varying experience levels, not all the elevation differences are the same quality. Their results and expected uncertainties are listed in the table. What is the most probable elevation difference and its uncertainty?
Crew 
Elev Diff, ft 
σ, ft 
1 
5.36 
±0.05 
2 
5.41 
±0.08 
3 
5.37 
±0.04 
4 
5.43 
±0.12 
Answers