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 (B)</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 (B)</p> Signup and view all the answers

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

<p>True (A)</p> Signup and view all the answers

Flashcards

Precision

Closeness of repeated measurements to each other.

Accuracy

Closeness of a measurement to its true value.

Theory of Probability

The probability of an event is the number of times it is likely to occur out of a total number of possible occurrences.

Systematic Errors

Errors that are not random, but follow a pattern and can be expressed using a mathematical relationship.

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Gross Errors

Errors that occur due to carelessness or mistakes by the surveyor.

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Random Errors

Random errors happen unpredictably and cannot be precisely predicted. They are inherent in every measurement.

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Most Probable Value (x̄)

The best estimate of the true value of a measured quantity. It is calculated by averaging multiple observations.

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Residual or Deviation (v)

The difference between a measured value and the most probable value of a quantity.

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Standard Deviation (δn)

A measure of dispersion or spread in a distribution. It tells us how much the data points are scattered around the mean.

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Sample Standard Deviation (SD)

An estimate of the population standard deviation based on a sample of measurements.

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Standard Error of the Mean (SEm)

A measure of the precision of the mean of a set of measurements. It tells us how much the sample mean is likely to vary from the true mean.

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Probable Error of a Single Measurement (PES)

The error for which there are equal chances of the true error being greater or less than it.

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Probable Error of the Mean Measurement (PEm)

The probable error of the mean is the error within which the true value of the mean is likely to lie.

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Variance (V)

Represents how much the data varies around the mean. Larger variance means data is more scattered.

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Relative Precision (RP)

The ratio of the probable error of the mean to the mean itself. Expresses the precision of a measurement.

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Weight (W) of a Measurement

A value that reflects the reliability of a measurement, with higher weight indicating higher reliability.

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Adjustments of Weighted Observations

The process of finding the most probable value of a quantity when multiple measurements of varying reliability are available.

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Weight (W) Formula for Weighted Observations

Derived from the probable error of a measurement. It is inversely proportional to the square of the probable error.

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Weight (W) Proportionality to Number of Observations

The weights of a measurement are directly proportional to the number of observations used to obtain that measurement.

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Weighted Mean (x̅m)

A way of combining multiple measurements of unequal reliability to get a single, more precise measurement. It gives more importance to measurements with higher weights.

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Field Measurement

A measurement that is taken in the field using surveying instruments to determine distances, angles, or elevations.

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Survey Line

A series of measurements taken in a specific order to create a complete picture of the area being surveyed.

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Survey Adjustments

Mathematical functions used to adjust the measurements for errors, ensuring the final representation of the area is accurate and consistent.

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Area Calculation

The process of calculating the area enclosed by the survey lines based on the adjusted measurements.

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Control Data

Information that can be used to verify the accuracy of the measurements and the overall surveying process.

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Survey Plan

A mathematical representation of the surveyed area, often drawn on a map or plan.

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Traverse

A method of establishing a network of control points or other survey features. It helps determine their precise positions and relationships.

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Electronic Distance Measurement (EDM)

A method of distance measurement that leverages the reflection of light or a signal to determine distances.

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Triangulation

A method of surveying that uses a series of connected lines to determine the relative positions of points.

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Coordinate Determination

A method of determining a specific location using a series of measurements and calculations.

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Horizontal Control

The process of transferring horizontal positions from a control network to other points in the survey.

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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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PCE1 Fundamentals of Surveying - Chapter 1 PDF

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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