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12 Instructor’s Solution Manual
Elementary Surveying: An Introduction to Geomatics
3 THEORY OF ERRORS IN OBSERVATIONS
3.1 Discuss the difference between an error and a residual.
From Section 3.3, an error is the difference between the observation and its true value,
3.2 Give two examples of (a) direct and (b) indirect measurements.
From Section 3.2: A direct observation is made by applying a measurement instrument
3.3 Define the term systematic error, and give two surveying examples of a systematic error.
3.4 Define the term random error, and give two surveying examples of a random error.
3.5 Discuss the difference between accuracy and precision.
3.6 The observations of 124.53, 124.55, 142.51, and 124.52 are obtained when taping the
length of a line. What should the observer consider doing before a mean length is
determined from the set of observations?
3.8 Same as Problem 3.7 but discard only one 65.396 observation.
3.9 Same as Problem 3.7, but discard both 65.396 observations.
3.10 Same as Problem 3.7, but include two additional observations, 65.402 and 65.405.
(a) 65.402 ∑784.819
3.11 For the data of Problem 3.7.
3.12 For the data of Problem 3.8.
3.13 For the data of Problem 3.9.
3.14 For the data of Problem 3.10.
(a) 65.4016±0.0053 (65.3963, 65.4069), 83.3%, both 65.396 outside of range
*3.15 23°30′00″,23°30′10″,23°30′10″, and 23°29′55″.
3.16 Same as Problem 3.15, but with three additional observations, 23°29′55″,23°29′50″
and 23°30′05″.
3.17 Same as Problem 3.15, but with two additional observations, 23°30′05″ and
23°29′55″.
3.18* A field party is capable of making taping observations with a standard deviation of ±0.02
ft per 100 ft tape length. What standard deviation would be expected in a distance of
400 ft taped by this party?
3.19 Repeat Problem 3.18, except that the standard deviation per 30-m tape length is ±3mm
and a distance of 60 m is taped. What is the expected 95% error in 60 m?
3.20 A distance of 200 ft must be taped in a manner to ensure a standard deviation smaller
than ±0.04 ft. What must be the standard deviation per 100 ft tape length to achieve the
desired precision?
3.21 Lines of levels were run requiring n instrument setups. If the rod reading for each
backsight and foresight has a standard deviation σ, what is the standard deviation in each
of the following level lines?
3.22 A line AC was observed in 2 sections AB and BC, with lengths and standard deviations
listed below. What is the total length AC, and its standard deviation?
(3.11)
3.23 Line AD is observed in three sections, AB, BC, and CD, with lengths and standard
32.08, and 32.01 ft. The observations were given weights of 2, 1, 3 and 2, respectively,
by the observer. *(a) Calculate the weighted mean for distance AB. (b) What difference
results if later judgment revises the weights to 2, 3, 1, and 1, respectively?
3.25 Determine the weighted mean for the following angles:
3.26 Specifications for observing angles of an n-sided polygon limit the total angular
misclosure to E. How accurately must each angle be observed for the following values
of n and E?
3.27 What is the area of a rectangular field and its estimated error for the following recorded
values:
By Equation (3.13):
3.28 Adjust the angles of triangle ABC for the following angular values and weights:
By Equation (3.17):
