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?

An error that can be treated mathematically Signup and view all the answers

Why is it difficult to completely eliminate gross errors?

Because they are due to human mistakes Signup and view all the answers

What is a random error?

An error that occurs due to environmental factors Signup and view all the answers

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

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

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

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

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

To determine the precision of the instrument used in measurement Signup and view all the answers

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

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

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

The standard deviation is the square root of the variance Signup and view all the answers

What is the limiting error of a measuring instrument?

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

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

It increases Signup and view all the answers

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

Inherent shortcomings of the instrument Signup and view all the answers

What can rectify systematic errors in measurement?

Correcting the measurement instrument Signup and view all the answers

What is the average deviation expressed as?

Absolute values of the deviations divided by the number of readings Signup and view all the answers

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

Systematic error due to misuse of the instrument Signup and view all the answers

What is the primary purpose of calculating the standard deviation?

To describe the spread of a dataset Signup and view all the answers

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

The standard deviation is the square root of the variance Signup and view all the answers

What can avoid instrumental errors due to inherent shortcomings?

Carefully planning the measurement procedure Signup and view all the answers

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

It always reads too high Signup and view all the answers

What is an example of an environmental error?

Aging of the instrument Signup and view all the answers

What can rectify instrumental errors due to inherent shortcomings?

Recalibrating the instrument Signup and view all the answers

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

The device always reads too high 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?

Because systematic errors are large compared to random errors Signup and view all the answers

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

It results in a random error Signup and view all the answers

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

To reduce random errors Signup and view all the answers

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

When the number of readings is very large 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?

Not specified in the text Signup and view all the answers

What is the characteristic of a residual error?

It remains even after the elimination of other types of errors Signup and view all the answers

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

Zero Signup and view all the answers

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

To determine the uncertainty of the final test result 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?

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

What does the example from the analogue meter measurement show?

The measurements are affected by random errors 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?

To understand the distribution of the readings Signup and view all the answers

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

It affects the accuracy of the measurement Signup and view all the answers

What is being measured in Example B1?

Current flowing in a circuit 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?

To understand the distribution of the resonant frequency readings Signup and view all the answers

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

The circuit is not in a steady state Signup and view all the answers

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

The type of circuit affects the accuracy of the measurement 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.