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(b) mistakes in reading graduated scales, and (c) mistakes in recording
(i.e., writing down 27.55 for 25.75). Mistakes are also known as blunders
or gross errors.
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4 INTRODUCTION
2. Systematic errors. These errors follow some physical law and thus can
be predicted. Some systematic errors are removed by following correct
observational procedures (e.g., balancing backsight and foresight distances
in differential leveling to compensate for Earth curvature and refraction).
Others are removed by deriving corrections based on the physical condi tions that were responsible for their creation (e.g., applying a computed
correction for Earth curvature and refraction on a trigonometric leveling
observation). Additional examples of systematic errors are (a) temperature
not being standard while taping, (b) an indexing error of the vertical circle
of a total station instrument, and (c) use of a level rod that is not of standard
length. Corrections for systematic errors can be computed and applied to
observations to eliminate their effects.
3. Random errors. These are the errors that remain after all mistakes and
systematic errors have been removed from the observed values. In general,
they are the result of human and instrument imperfections. They are gen erally small and are as likely to be negative as to be positive. They usually
do not follow any physical law and therefore must be dealt with according
to the mathematical laws of probability. Examples of random errors are
(a) imperfect centering over a point during distance measurement with an
EDM instrument, (b) bubble not centered at the instant a level rod is read,
and (c) small errors in reading graduated scales. It is impossible to avoid
random errors in measurements entirely. Although they are often called
accidental errors, their occurrence should not be considered an accident.
1.5 PRECISION VERSUS ACCURACY
Due to errors, repeated measurement of the same quantity will often yield dif ferent values. A discrepancy is defined as the algebraic difference between
two observations of the same quantity. When small discrepancies exist between
repeated observations, it is generally believed that only small errors exist. Thus,
the tendency is to give higher credibility to such data and to call the observa tions precise. However, precise values are not necessarily accurate values. To
help demonstrate the difference between precision and accuracy, the following
definitions are given:
1. Precision is the degree of consistency between observations and is based
on the sizes of the discrepancies in a data set. The degree of precision
attainable is dependent on the stability of the environment during the time
of measurement, the quality of the equipment used to make the obser vations, and the observer s skill with the equipment and observational
procedures.
2. Accuracy is the measure of the absolute nearness of an observed quantity
to its true value. Since the true value of a quantity can never be determined,
accuracy is always an unknown.
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1.5 PRECISION VERSUS ACCURACY 5
The difference between precision and accuracy can be demonstrated using
distance observations. Assume that the distance between two points is paced,
taped, and measured electronically and that each procedure is repeated five times.
The resulting observations are:
Observation Pacing (p) Taping (t) EDM (e)
1 571 567.17 567.133
2 563 567.08 567.124