Q.Explain, with a simple example, the difference between the accuracy and the precision of a set of measurements.

[!TLDR] Accuracy is closeness to the true value; precision is closeness among repeated readings. [!ANSWER] A set of readings can be precise (tightly clustered) yet inaccurate (offs …

Accuracy measures how close a measured value is to the actual, true value of the quantity. Precision measures how close repeated measurements of the same quantity are to each other, regardless of whether that shared value is correct.

Worked example. Suppose the true mass of an object is exactly $10.00$ g, and it is weighed three times on a balance:

• If the balance reads $10.62$ g, $10.61$ g, $10.63$ g — the three readings are extremely close to each other (a spread of only $0.02$ g), so the balance is precise. But every reading is about $0.6$ g away from the true value of $10.00$ g, so the balance is not accurate — most likely because of an uncorrected zero error, a systematic error.
• If instead the balance reads $9.85$ g, $10.20$ g, $9.95$ g — these readings vary more amongst themselves (less precise), but their average, $\approx10.00$ g, is very close to the true value, so the balance is reasonably accurate on average. …

Define accuracy and precision separately, then construct one numeric example where readings are tightly clustered but offset from the true value (pr …

• Treating 'accurate' and 'precise' as synonyms in everyday usage, rather than as two independent, separately-defined technical terms …