#### 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

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 EMPV 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 v2 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 v2 Width v v2 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 EMPV are 3 sf, including an additional one for intermediate calculations.

Since length and width should both have 4 sf, Area = 5215 yd2.

Since additional sf were carried for L, W, and their EMPVs, the area error should be expressed to 2 sf: Error = ±10. yd2.

5215 yd2 ±10. yd2

#### 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 (n-2)x180°, how much error is allowed in each angle of a five-sided 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”