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'.

Meas
v
v2
118.54
+0.027
0.000729
118.52
+0.007
0.000049
118.48
0.033
0.001089
118.54
+0.027
0.000729
118.53
+0.017
0.000289
118.47
0.043
0.001849
sums:
711.08
0.004734
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?
Crew A had better precision because its standard deviation was lower.
Expected accuracy?
Must compute and compare EMPV for each crew
Crew B had better expected accuracy since its E_{MPV} was lower.
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".
Subtract 37°18' from each angle to work with just seconds.

Angle
Sec
v
v^{2}
37°18'55"
55
05.6
31.36
37°19'04"
64
+03.4
11.56
37°19'09"
69
+08.4
70.56
37°18'53"
53
07.6
57.76
37°19'02"
62
+01.4
1.96
sums:
303
173.20
Problem (4)
The length and width of a building are measured in feet, summarized in the table below.
What are the building's area and expected area error in square yards?

Length
v
v^{2}
Width
v
v^{2}
173.9
0.33
0.109
89.6
0.20
0.040
174.5
+0.27
0.073
90.1
0.30
0.090
174.3
+0.07
0.005
89.7
0.10
0.010
sums:
522.7
0.187
269.4
0.140
The length sum has 4 sf, its average will have 4 sf.
The width sum has 4 sf, its average will have 4 sf.
Carry one more sf for each MPV to minimize intermediate rounding.

Length:
Width:
Each SD and E_{MPV} are 3 sf, including an additional one for intermediate calculations.
Since length and width should both have 4 sf, Area = 5215 yd^{2}.
Since additional sf were carried for L, W, and their E_{MPV}s, the area error should be expressed to 2 sf: Error = ±10. yd^{2}.
5215 yd^{2} ±10. yd^{2}
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?
Because a subtraction is involved, must use Error of a Sum. Carry additional sf for the error comps.
30.5 gr ±0.8 gr
Problem (6)
If all angles are measured to the same level of accuracy and their total must be within 15 seconds of (n2)x180°, how much error is allowed in each angle of a fivesided property?
Since all angle measurements will have the same expected error, use Error of a Series and solve backwards.
Because 15” has 2 sf: Error = ±6.7”