Accuracy And Precision

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Repeated measurements of a standard 50.0 gram mass cluster tightly between 46.9 gram and 47.1 gram across many trials; how is this set of data best characterised?

RankGuru · Accepted Answer

Accuracy and precision describe two distinct aspects of measurement quality and must not be confused. Accuracy refers to how close measurements lie to the true value, while precision refers to how closely repeated measurements agree with one another, regardless of the true value. In the given data, the readings span only 46.9 to 47.1 gram, a very narrow band, which signals high precision because the trials reproduce one another closely. However, every reading sits well below the true value of 50.0 gram by about three grams, revealing a systematic offset and therefore poor accuracy. Hence the set is precise but not accurate. The choice accurate and precise is wrong because the readings are systematically far from the true value. The choice accurate but not precise contradicts both observations, since the spread is small and the centre is off-target. The choice neither accurate nor precise fails because the tight clustering clearly demonstrates good precision. This distinction is emphasised in the NCERT measurement chapter. A sanity check: a consistent low bias like this usually points to a systematic error such as an uncalibrated balance.

Accuracy And Precision

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