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 $10.00$ g.

• A balance that repeatedly reads $10.62$ g, $10.61$ g, $10.63$ g is precise (the readings are tightly clustered) but not accurate (they are all offset from the true value by about $0.6$ g — this offset is a systematic error, e.g. from an uncorrected zero error).
• A balance that reads $9.85$ g, $10.20$ g, $9.95$ g, $10.15$ 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). …