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What does precision refer to in surveying?
What does precision refer to in surveying?
The degree of closeness or conformity of repeated measurements of the same quantity to each other.
What does accuracy refer to in surveying?
What does accuracy refer to in surveying?
The degree of conformity of a measurement to its true value.
What is the definition of probability in surveying?
What is the definition of probability in surveying?
The theory of probability is based on the assumption that small errors are less likely than large ones.
The theory of probability is based on the assumption that small errors are less likely than large ones.
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What are gross errors?
What are gross errors?
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What are systematic errors?
What are systematic errors?
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What are random errors?
What are random errors?
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How is the most probable value (x) calculated?
How is the most probable value (x) calculated?
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What is the residual in surveying?
What is the residual in surveying?
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What is standard deviation?
What is standard deviation?
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What does the standard deviation formula calculate?
What does the standard deviation formula calculate?
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What is standard error of the mean?
What is standard error of the mean?
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What is the probable error?
What is the probable error?
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What is variance?
What is variance?
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What is relative precision?
What is relative precision?
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What is a weighted observation?
What is a weighted observation?
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The weights of weighted observations are directly proportional to the square of the corresponding probable errors.
The weights of weighted observations are directly proportional to the square of the corresponding probable errors.
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The weights of weighted observations are proportional to the number of observations.
The weights of weighted observations are proportional to the number of observations.
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Study Notes
Precision and Accuracy
- Precision is how close repeated measurements are to each other
- Accuracy is how close a measurement is to the true value
Probability Theory
- Probability is the frequency of an event occurring
- Probability theory is used to estimate measurement precision
- Assumptions about errors:
- Small errors are more probable than large errors
- Large errors are less probable
- Positive and negative errors of the same magnitude have equal probability
Error Types
- Gross errors: Mistakes, not true errors (e.g., carelessness)
- Systematic errors: Follow a pattern, can be corrected
- Random errors: Treated using probability models, inherent in observations
Most Probable Value (MPV)
- MPV is the best estimate of the true value
- Calculated as the mean of observations: (Σ(x * n)) / Σ(n)
- Residual (deviation): The difference between a measured value and the MPV (v = x - x)
Standard Deviation
- Measures the spread of data around the mean (Root-Mean Square Error)
- Calculates the average distance of each observation from the MPV
- Estimated using sample data (σ ≈ √(Σ(x-x)²)/(n-1))
Standard Error of the Mean
- Improves precision by averaging multiple observations
- Calculates the error associated with the mean of the observations
- (SEm ≈ √(Σ(x-x)²)/(n * (n-1))) , (where n is the number of observations)
Probable Error of Single Measurement
- PE is a defined error for which there are equal chances of the true error being less and greater than the probable error.
- Calculated as ±0.6745 * √(Σ(x-x)²)/(n - 1))
Probable Error of Mean Measurement
- PEm is the error associated with the average of multiple measurements
- Calculated as ±0.6745 * √(Σ(x-x)²)/(n * (n-1)) where n is the number of measurements
Variance
- Variance (V) measures the dispersion of data spread
- Calculated as Σ(x − x)² / (n − 1), n = number of observations
Relative Precision
- Relative error or Relative Precision is given as a fraction, with measured value in denominator.
- Used to determine the degree of refinement of a result
Weighted Observations
- Weights (W) indicate the reliability of measurements
- Weights are inversely proportional to the square of the probable errors of the corresponding measurements. The weights are also directly proportional to the number of observations.
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Description
This quiz focuses on the essential concepts of measurement precision and accuracy, probability theory, and various types of errors in measurements. It will cover how to estimate measurements and understand the Most Probable Value. Test your knowledge and grasp the importance of these statistical principles.