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# Elementary Surveying

### Elementary Surveying: Ch. 3 Theory of Errors in Observations

Question | Answer |
---|---|

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 |