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 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”

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