ECE 251: Measurements and Instrumentation Chapter 3
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Questions and Answers

What is the definition of error in measurement?

  • The true or actual value of a quantity
  • The sum of gross, systematic and random errors
  • The difference between the true or actual value and the measured value (correct)
  • The ratio of true value to measured value

    • What is the main cause of gross errors?

  • Instrumental defects
  • Random fluctuations
  • Human mistakes in reading or using instruments (correct)
  • Environmental factors

    • What is an example of a gross error?

  • Reading a temperature as 21.5° C when the actual value is 31.5° C
  • Using a faulty instrument
  • Recording a value as 34.5° C when the actual value is 35.4° C
  • All of the above (correct)

    • What is a systematic error?

    <p>An error that can be treated mathematically</p> Signup and view all the answers

    Why is it difficult to completely eliminate gross errors?

    <p>Because they are due to human mistakes</p> Signup and view all the answers

    What is a random error?

    <p>An error that occurs due to environmental factors</p> Signup and view all the answers

    What is the main difference between gross errors and systematic errors?

    <p>Gross errors are due to human mistakes, while systematic errors can be treated mathematically</p> Signup and view all the answers

    What is the main difference between instrumental error and environmental error?

    <p>Instrumental error is due to instrumental defects, while environmental error is due to environmental factors</p> Signup and view all the answers

    What is the primary purpose of calculating the average deviation in statistical analysis?

    <p>To determine the precision of the instrument used in measurement</p> Signup and view all the answers

    What is the formula for calculating the standard deviation of an infinite number of data?

    <p>Square root of the sum of individual deviations squared divided by the number of readings</p> Signup and view all the answers

    What is the relationship between the variance and the standard deviation?

    <p>The standard deviation is the square root of the variance</p> Signup and view all the answers

    What is the limiting error of a measuring instrument?

    <p>The accuracy of the instrument within a certain percentage of full-scale reading</p> Signup and view all the answers

    How does the limiting error change with a reading less than full scale?

    <p>It increases</p> Signup and view all the answers

    What is the main reason for Instrumental Error in a measuring instrument?

    <p>Inherent shortcomings of the instrument</p> Signup and view all the answers

    What can rectify systematic errors in measurement?

    <p>Correcting the measurement instrument</p> Signup and view all the answers

    What is the average deviation expressed as?

    <p>Absolute values of the deviations divided by the number of readings</p> Signup and view all the answers

    What is the result of failing to adjust the zero of an instrument?

    <p>Systematic error due to misuse of the instrument</p> Signup and view all the answers

    What is the primary purpose of calculating the standard deviation?

    <p>To describe the spread of a dataset</p> Signup and view all the answers

    What is the relationship between the variance and the standard deviation of a finite number of data?

    <p>The standard deviation is the square root of the variance</p> Signup and view all the answers

    What can avoid instrumental errors due to inherent shortcomings?

    <p>Carefully planning the measurement procedure</p> Signup and view all the answers

    What is the effect of inherent shortcomings of an instrument on its measurement?

    <p>It always reads too high</p> Signup and view all the answers

    What is an example of an environmental error?

    <p>Aging of the instrument</p> Signup and view all the answers

    What can rectify instrumental errors due to inherent shortcomings?

    <p>Recalibrating the instrument</p> Signup and view all the answers

    What is the result of a permanent magnet's spring becoming weak?

    <p>The device always reads too high</p> Signup and view all the answers

    What is the primary reason why statistical analysis of data cannot remove a fixed bias contained in all measurements?

    <p>Because systematic errors are large compared to random errors</p> Signup and view all the answers

    What is the consequence of a sudden change in experimental conditions during an experiment?

    <p>It results in a random error</p> Signup and view all the answers

    What is the purpose of taking the average of a large number of readings?

    <p>To reduce random errors</p> Signup and view all the answers

    What is the condition for the arithmetic mean to be the best approximation of a measured variable?

    <p>When the number of readings is very large</p> Signup and view all the answers

    What is the expression for the arithmetic mean of n measurements at a specific count of the variable x?

    <p>Not specified in the text</p> Signup and view all the answers

    What is the characteristic of a residual error?

    <p>It remains even after the elimination of other types of errors</p> Signup and view all the answers

    What is the algebraic sum of all the deviations from the mean?

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

    What is the primary purpose of statistical analysis of measurement data?

    <p>To determine the uncertainty of the final test result</p> Signup and view all the answers

    What is the reason for a well-calibrated voltmeter giving a misleading resistance reading in a high-resistance circuit?

    <p>The circuit has a high resistance which affects the voltmeter's reading</p> Signup and view all the answers

    What does the example from the analogue meter measurement show?

    <p>The measurements are affected by random errors</p> Signup and view all the answers

    What is the purpose of calculating the mean value, deviations from the mean, and standard deviation in the measurement readings?

    <p>To understand the distribution of the readings</p> Signup and view all the answers

    Why is it important to consider the loading effect of a voltmeter in a circuit?

    <p>It affects the accuracy of the measurement</p> Signup and view all the answers

    What is being measured in Example B1?

    <p>Current flowing in a circuit</p> Signup and view all the answers

    What is the purpose of calculating the arithmetic mean, deviations from mean, average deviation, standard deviation, and variance in the resonant frequency readings?

    <p>To understand the distribution of the resonant frequency readings</p> Signup and view all the answers

    What can be inferred about the circuit in which the analogue meter measurements were taken?

    <p>The circuit is not in a steady state</p> Signup and view all the answers

    Why is it important to consider the type of circuit when using a voltmeter?

    <p>The type of circuit affects the accuracy of the measurement</p> Signup and view all the answers

    Study Notes

    Errors in Measurements and Their Statistical Analysis

    • Errors in measurement are defined as the difference between the true or actual value and the measured value.
    • Sources of error in measurement include:
      • Gross error
      • Systematic error
      • Random error

    Types of Static Error

    • Gross Errors:
      • Due to human mistakes in reading or using instruments, or errors in recording observations.
      • Examples: improper use of an instrument, incorrect adjustment of instruments, computational mistakes.
      • Minimization can be achieved by taking more care while reading and recording data, and by taking more readings of the quantity under measurement by different experimenters.
    • Systematic Errors:
      • Due to the presence of a fault in the measuring instrument, environmental effects, or observational errors.
      • Can be classified into:
        • Instrumental error
        • Environmental error
        • Observational error
      • Can be corrected by rectifying the measurement instrument.
    • Random Errors:
      • Caused by sudden changes in experimental conditions, noise, or tiredness of the experimenter.
      • Can be either positive or negative.
      • Can be reduced by taking the average of a large number of readings.

    Statistical Analysis

    • Arithmetic Mean:
      • The most probable value of a measured variable.
      • Calculated as the sum of all readings divided by the number of readings.
    • Deviation from the Mean:
      • The departure of a given reading from the arithmetic mean of the group of readings.
      • Can be positive or negative.
      • The algebraic sum of all deviations is zero.
    • Average Deviations:
      • An indication of the precision of the instrument used in measurement.
      • Calculated as the sum of the absolute values of the deviation divided by the number of readings.
    • Standard Deviation:
      • The square root of the sum of all individual deviations squared, divided by the number of readings.
    • Variance:
      • The mean square deviation, which is the same as the standard deviation, except that the square root is not extracted.

    Limiting Errors

    • Specified by manufacturers of measuring instruments as a percentage of a full-scale reading.
    • Example: A voltmeter may be specified to be accurate within ± 2% of a full-scale reading.

    Solved Examples

    • Examples of solved problems, including calculating mean value, deviations from the mean, and standard deviation.

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    Description

    This quiz covers chapter 3 of ECE 251, focusing on errors in measurements and their statistical analysis. It includes types of static errors and more.

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