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Elementary Surveying

Elementary Surveying: Ch. 3 Theory of Errors in Observations

True or False, observations are never exact and will always contain errors. True
Direct Observations Applying a tape to a line, a protractor to an angle, or turning an angle with a total station
Indirect Observations is secured when it is not possible to apply a measuring instrument directly to the quantity to be observed
Error the difference between an observed value for a quantity and its true value
Observer Blunders transposition of number, sighting the wrong target, mis-recording a measurement
Natural Errors caused by variations in wind, temperature, humidity, atmospheric pressure, atmospheric refraction, gravity and magnetic declination
Instrumental Errors results from imperfections, physical limitations, and improper adjustment of measurement instruments
Personal Errors arise from limitations of human senses of sight and touch
Systematic Errors cumulative errors, result from errors resulting from the environment, instrument and observer
Random Errors accidental errors, errors that remain after systematic errors have been removed
Discrepancy the difference between two observed values of the same quantity
Precision the degree of refinement or consistency of a group of observations and is evaluated on the basis of discrepancy size
Accuracy denotes the absolute nearness of observed quantities to their true value
True or false, comparing several observations of the same quantity is one of the best ways to identify mistakes true
Probability the ratio of the number of times a result should occur to its total number of possibilities
Most Probable Value used for multiple direct observations of the same quantity using the same equipment and procedures
Residuals the difference between the most probable value and any observed value of a quantity
Frequency number of times it occured
Dispersion range in observations from smallest to largest
Histogram bar graph
Class Interval the interval of residuals represented by each bar
Normal Distribution Curve shape of a histogram for a normally distributed data set that is very large; can be used to compute probability of occurrence of a measurement
What is the first law of probability? small residuals (errors) occur more often than large ones
What is the second law of probability? large residuals happen infrequently
What is the third law of probability? positive and negative residuals of the same size occur with equal frequency
Standard Deviation a measure of precision of a data set which is easier to evaluate in terms of the data set arithmetic mean; corresponds to an area under the normal distribution curve
Variance the square of the standard deviation
Percentage Error level of confidence that a computed MPV is close to the truth; based upon the area under the probability curve
Probable Error limits within which an observation should be 50% of the time
Standard Error estimate of the standard deviation i.e. the average error expected for any given measurement
2 Sigma Error commonly specified precision limit for measurement errors in surveying projects
3 Sigma Error common criterion for rejecting a measurement based upon the probable presence of a mistake or blunder
50 Percent Error 0.6745σ
68.3 Percent Error 1.0000σ
90 Percent Error 1.6449σ
95 Percent Error 1.9599σ
99.7 Percent Error 2.968σ
Error Propagation the process of evaluating errors in quantities computed from observed values that contain errors
True or False, observations weighted more heavily are more precise and considered to be closer to the true value true
True or False, observations with the greatest weight gets the smallest correction true
Created by: kristinestrong