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LECTURE 1

LECTURE 1. MEASUREMENT AND ERROR. CONTENTS. Definitions Accuracy and Precision Significant Figures Types of Error Statistical Analysis Probability of Errors Probable Error Limiting Errors Systems of Units of Measurement Standards of Measurement. Limiting Errors

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LECTURE 1

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  1. LECTURE 1 MEASUREMENT AND ERROR

  2. CONTENTS • Definitions • Accuracy and Precision • Significant Figures • Types of Error • Statistical Analysis • Probability of Errors • Probable Error • Limiting Errors • Systems of Units of Measurement • Standards of Measurement

  3. Limiting Errors • Systems of Units of Measurement • Standards of Measurement

  4. Definitions[CONTENTS] • Measurement : generally involves using an instrument as a physical means of determining a quantity or variable • Instrument : a device for determining the value or magnitude of a quantity or variable • Accuracy : closeness with which an instrument reading approaches the true value of the variable being measured. • Precision : a measure of the reproducibility of the measurements; i.e., given a fixed value of a variable, precision is a measure of the degree to which successive measurements differ from one another • Sensitivity : the ratio of output signal or response of the instrument to a change of input or measured variable. • Resolution : the smallest change in measured value to which th instrument will respond. • Error : deviation from the true value of the measured variable.

  5. Accuracy and Precision[contents] • Precision is composed of two characteristics : conformity and the number of significant figures to which a measurement may be made • Conformity is a necesary, but not sufficient, condition for precision because of the lack of significant figures obtained • Precision is a necesary, but not sufficient, condition for accuracy.

  6. Significant Figures[contents] • Significant figures convey actual information regarding the magnitude and the measurement precision of a quantity • The more significant figures, the greater the precision of the measurement • When a number of independent measurements are taken in an effort to obtain the best possible answer (closest the true value), the result is usually expressed as the arithmetic mean of all readings, with the range of possible error as the largest deviation from that mean • When two or more measurements with different degrees of accuracy are added, the result is only as accurate as the least accurate measurement.

  7. Types of Error[Contents] • Gross errors : largely human errors, among them misreading of instruments, incorrect adjustments, and computational mistakes. • Systematic errors : shortcomings of the instruments, such as defective or worn parts, and effects of the environment on equipment or the user. • Random errors : those due to causes that cannot be directly established because of random variations in the parameter or the system of measurement.

  8. Statistical Analysis[Contents] • Arithmetic mean • Deviation from the mean • Average deviation • Standard deviation • Standard deviation of a finite number of data

  9. Probability of Errors[Contents]

  10. Probable Error[Contents]

  11. Limiting Errors[Contents] • In most indicating instruments the accuracy is guaranteed to a certain percentage of full-scale reading. Circuit components (such as capacitors, resistors, etc.) are guaranteed within a certain percentage of their rated value. The limits of these deviations from the specified values are known as limiting errors or guarantee errors.

  12. System of Unit MeasurementsDesimal multiples and submultiples [1][Contents]

  13. Basic SI Quantities, Units, and Symbols [1]

  14. Electric and Magnetic Units [1]

  15. Fundamental, Supplementary, and Derived Units [1]

  16. English Into SI Conversion [1]

  17. Standards of Measurement[Contents] • Standard of measurement is a physical representation of a unit of measurement • Classification : • International standards • Primary standards • Secondary standards • Working standard

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