Measurement Errors and Standards Questions and Answers

Q: A measurement result should be reported as

Correct answer: a best estimate with a stated uncertaintyA result without an uncertainty cannot be used: the reader has no way to judge whether it agrees with another figure, meets a specification, or supports a conclusion. Reporting the best estimate together with its uncertainty, and the basis on which that uncertainty was arrived at, is what makes the measurement usable by someone else.

Q: Which of these is a random rather than a systematic source of error?

Correct answer: Thermal noise in a measuring circuitThermal noise is a fluctuating quantity of unpredictable sign, so it scatters readings about a mean and is reduced by averaging. The other three all shift the reading consistently in one direction - an uneven scale, a persistent temperature offset, a pointer off zero - and are systematic errors, correctable but not averageable.

41.

Assertion (A): A class 1.0 instrument should be read in the upper part of its range.

Reason (R): Its error is specified as a percentage of full scale.

Select the correct option.

A.A is false but R is true, such an instrument being best read at low deflection
B.Both A and R are true, and R is the correct explanation of A
C.Both A and R are true, but R is not the correct explanation of A at all
D.A is true but R is false, the error being a percentage of the reading

Answer: B

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the mechanism. The class figure fixes the permitted error as a fraction of full scale, so it is a constant number of volts or amperes wherever the pointer sits. Expressed as a fraction of the reading it therefore grows as the deflection falls - 1 per cent at full scale, 5 per cent at a fifth of it.

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42.

Assertion (A): A voltmeter of low resistance can give a badly wrong reading.

Reason (R): It draws current and changes the voltage it is measuring.

Select the correct option.

A.A is true but R is false, a voltmeter drawing no current at all
B.A is false but R is true, meter resistance being of no consequence
C.Both A and R are true, and R is the correct explanation of A
D.Both A and R are true, but R is not the correct explanation of A at all

Answer: C

Shunting a high-impedance circuit alters the very quantity under measurement, and the error can be tens of per cent. The reason is the mechanism, and it is why input impedance appears on every voltmeter's specification.

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43.

True or false: a more expensive instrument is necessarily more accurate.

A.True, since price and accuracy are directly related in instruments
B.True, provided the instrument is of the digital rather than analogue kind
C.False, since price has no bearing on any property of an instrument
D.False, since accuracy depends on calibration and on suitability for the task

Answer: D

Correct answer: False, since accuracy depends on calibration and on suitability for the task

Price correlates loosely with quality but guarantees nothing: an expensive instrument out of calibration, or applied where it loads the circuit, gives a worse result than a cheap one used properly. What determines accuracy is a valid calibration, an appropriate range, and a measurement method that does not disturb what it measures.

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44.

True or false: adding more digits to a display improves the accuracy of a measurement.

A.False, since resolution and accuracy are different properties
B.True, since more digits means a more accurate reading
C.True, provided the instrument has been recently calibrated
D.False, since more digits reduces the accuracy of the reading

Answer: A

Correct answer: False, since resolution and accuracy are different properties

Extra digits let the instrument discriminate finer changes, which is resolution. Whether those digits are correct is accuracy, and that depends on calibration. A five-digit meter that is 1 per cent out displays its error to five figures - the additional digits make the wrong answer more precise, not more right.

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45.

A measurement result should be reported as

A.the mean of many readings quoted without qualification
B.a best estimate with a stated uncertainty
C.the indicated reading alone
D.the largest and smallest readings obtained during the test

Answer: B

Correct answer: a best estimate with a stated uncertainty

A result without an uncertainty cannot be used: the reader has no way to judge whether it agrees with another figure, meets a specification, or supports a conclusion. Reporting the best estimate together with its uncertainty, and the basis on which that uncertainty was arrived at, is what makes the measurement usable by someone else.

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46.

Rounding a result to fewer figures than the uncertainty warrants

A.is always preferable to quoting too many figures
B.has no consequence of any kind for the reader
C.throws away information the measurement actually contains
D.improves the apparent accuracy of the measurement

Answer: C

Correct answer: throws away information the measurement actually contains

Over-rounding is as much a fault as quoting spurious figures, though a less conspicuous one. If the uncertainty is 0.02 then quoting 12.3 discards a digit the measurement genuinely determined. The convention is to round the uncertainty to one or two significant figures and match the result to the same decimal place.

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47.

The zero error of an instrument is

A.a random error reducible only by averaging
B.a gross error arising from the observer's mistake
C.an environmental error caused by temperature change
D.a systematic error correctable by adjustment

Answer: D

A pointer resting off zero shifts every reading by the same amount, which is the definition of a systematic error, and the adjuster exists to remove it. Checking it before and after a set of readings is standard practice.

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48.

Checking an instrument's zero after a set of readings as well as before is worth doing because

A.a drift during the readings would otherwise go unnoticed
B.the zero cannot be checked before readings are taken
C.the second check improves the resolution of the instrument
D.standards require every instrument to be zeroed twice

Answer: A

Correct answer: a drift during the readings would otherwise go unnoticed

Checking the zero at both ends brackets the readings: if it has moved, the readings taken between are suspect and can be corrected or repeated. Checking only beforehand assumes stability over the whole session, which for a sensitive instrument warming up or in a changing ambient is not a safe assumption.

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49.

The uncertainty of a measurement made with a calibrated instrument includes

A.neither
B.the calibration uncertainty as well as the instrument's own error
C.only the instrument's specified error
D.only the calibration uncertainty

Answer: B

The correction from the certificate is itself uncertain, and that uncertainty is inherited by every measurement made with the instrument. It is one link in the traceability chain and has to be combined with the others.

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50.

Which of these is a random rather than a systematic source of error?

A.A scale divided slightly unevenly at manufacture
B.An ambient temperature consistently above the calibration value
C.Thermal noise in a measuring circuit
D.A pointer resting off its zero position

Answer: C

Correct answer: Thermal noise in a measuring circuit

Thermal noise is a fluctuating quantity of unpredictable sign, so it scatters readings about a mean and is reduced by averaging. The other three all shift the reading consistently in one direction - an uneven scale, a persistent temperature offset, a pointer off zero - and are systematic errors, correctable but not averageable.

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