Measurement Errors and Standards Questions and Answers

Answer: A

Correct answer: how close its reading is to the true value

Accuracy is a statement about correctness, and it requires a reference - the true value, or the best available approximation to it from a standard. An instrument reading consistently 2 per cent high is inaccurate however repeatable its readings are, which is the distinction from precision.

Answer: B

Correct answer: how closely repeated readings of the same quantity agree

Precision is about scatter alone and says nothing about correctness. An instrument can be very precise and quite wrong - a systematic offset repeats faithfully in every reading. Precision is what averaging improves; accuracy is what calibration establishes.

Answer: C

Correct answer: the smallest change in input it can detect

Resolution is the fineness of discrimination: on a digital instrument, one count of the least significant digit; on an analogue one, the smallest scale division that can be judged. It is often confused with accuracy, but adding digits to a display improves only the resolution.

Answer: D

A sensitive instrument gives a large deflection for a small input, which is a different property from being able to resolve a small change. The two are often confused because a sensitive instrument is usually well resolved.

Answer: A

Every measurement carries an uncertainty, so the best that can be offered is an estimate with a stated interval around it. Treating the mean of many readings as the truth ignores any systematic error present in all of them.

Answer: B

Correct answer: the indicated value less the true value

\[ e = A_m - A_t. \] The sign convention matters: an instrument reading high has a positive error, and the correction to be applied is therefore negative. Reversing the order gives the correction rather than the error, which is why calibration certificates state explicitly which they are quoting.

Answer: C

Correct answer: human mistakes in reading or recording

Gross errors are blunders - misreading a scale, transposing digits, recording against the wrong entry, using the wrong range. They are not amenable to statistical treatment, since they are not small and not random, and the only defence is care and independent repetition by another observer.

Answer: D

Because it acts the same way each time, averaging does nothing at all for it, and only calibration against a standard reveals it. It is the more dangerous of the two kinds precisely because the readings look consistent.

Answer: A

Correct answer: scatters the readings about a mean value

Random errors arise from many small unpredictable influences and are as likely to be positive as negative, so the readings scatter symmetrically about a mean. This is precisely what makes them tractable: averaging converges on the mean, and the spread can be characterised by a standard deviation. A systematic error does neither.

Answer: B

Correct answer: random error but not systematic error

Averaging works on random error because positive and negative departures cancel, reducing the standard deviation of the mean by \( \sqrt{n} \). A systematic error shifts every reading the same way, so it survives the averaging untouched - taking a thousand readings on a miscalibrated instrument gives a very precise wrong answer.