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Physics · Ch 1 — Physical World and Measurement

Accuracy and Precision of Measuring Instruments

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Accuracy and Precision of Measuring Instruments

Two Different Qualities of a Measurement

It is tempting to think that a "good" measurement is simply one made with a fine instrument,

but two genuinely different qualities are actually involved:

  • Accuracy describes how close a measured value is to the true value of the quantity being measured. An accurate measurement has a small error (the difference between the measured and true values).
  • Precision describes how close repeated measurements of the same quantity are to one another — i.e. how reproducible the measurement is, regardless of whether the value they cluster around is actually correct. A precise measurement has a small spread (scatter) among repeated readings.

Crucially, a measurement can be precise without being accurate, and (less commonly) can

happen to be accurate on average while being imprecise. The four-panel target diagram in this

section makes the distinction visual.

Illustration: Weighing an Object

Suppose the true mass of an object is exactly 10.0010.00 g.

  • A balance that repeatedly reads 10.6210.62 g, 10.6110.61 g, 10.6310.63 g is precise (the readings are tightly clustered) but not accurate (they are all offset from the true value by about 0.60.6 g — this offset is a systematic error, e.g. from an uncorrected zero error).
  • A balance that reads 9.859.85 g, 10.2010.20 g, 9.959.95 g, 10.1510.15 g is scattered around close to the true value on average, so it is reasonably accurate, but it is not precise (the individual readings disagree with each other considerably). …
Figure 1Accuracy vs. precision (target diagram)

What this figure shows. A four-panel target/dartboard diagram, the classic own-drawn illustration of accuracy versus precision. Panel (a) shows a tight cluster of hits at the bull's-eye centre — both accurate and precise. Panel (b) shows a tight cluster of hits away from the centre, all in one corner of the board — precise (highly repeatable, low random error) but not accurate (a systematic offset from the true value). Panel (c) shows hits scattered widely but centred roughly on the bull's-eye — accurate on average but not precise (large random error, no systematic bias). Panel (d) shows hits scattered widely and off-centre — neither accurate nor precise. …