Measurement Precision and Accuracy
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Questions and Answers

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?

The degree of conformity of a measurement to its true value.

What is the definition of probability in surveying?

  • The number of times something will probably occur. (correct)
  • The likelihood of an event occurring.
  • The precision of results.
  • The range of possible occurrences.
  • The theory of probability is based on the assumption that small errors are less likely than large ones.

    <p>False</p> Signup and view all the answers

    What are gross errors?

    <p>Mistakes made due to carelessness of the observer.</p> Signup and view all the answers

    What are systematic errors?

    <p>Errors that follow a pattern and can be expressed by functional relationships.</p> Signup and view all the answers

    What are random errors?

    <p>Errors treated using a probability model.</p> Signup and view all the answers

    How is the most probable value (x) calculated?

    <p>Sum of the product of observed value and number of observations divided by the total number of observations.</p> Signup and view all the answers

    What is the residual in surveying?

    <p>The difference between any measured value of a quantity and its most probable value.</p> Signup and view all the answers

    What is standard deviation?

    <p>A measure of spread of distribution for a population, assuming the observations are of equal reliability.</p> Signup and view all the answers

    What does the standard deviation formula calculate?

    <p>The square root of the sum of the squares of the differences between each observation and the mean, divided by the number of observations minus one.</p> Signup and view all the answers

    What is standard error of the mean?

    <p>A measure of the precision of the mean, taking into account the number of observations.</p> Signup and view all the answers

    What is the probable error?

    <p>The error for which there are equal chances of the true error being less and greater than probable error.</p> Signup and view all the answers

    What is variance?

    <p>A measure of dispersion or spread of a distribution.</p> Signup and view all the answers

    What is relative precision?

    <p>The ratio of the probable error of the mean to the magnitude of a measured quantity.</p> Signup and view all the answers

    What is a weighted observation?

    <p>A measurement assigned a weight reflecting its reliability.</p> Signup and view all the answers

    The weights of weighted observations are directly proportional to the square of the corresponding probable errors.

    <p>False</p> Signup and view all the answers

    The weights of weighted observations are proportional to the number of observations.

    <p>True</p> Signup and view all the answers

    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.

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