Accuracy and Precision

Two words are often used loosely in everyday speech but mean two different things in measurement theory:

• Accuracy -- how close a measured value is to the true (theoretical) value.
• Precision -- how close repeated measurements are to each other, i.e. how reproducible the measurement is, regardless of whether they are close to the truth.

Worked example (temperature): suppose a refrigerator's real temperature is $9^\circ$C, and a thermometer repeatedly reads $10.4,10.2,10.3,10.1,10.2,10.1,10.1,10.1$ ($^\circ$C). All the readings cluster tightly around $10^\circ$C, so the thermometer is precise; but since $10^\circ$C is about $1^\circ$C off the true $9^\circ$C, it is not accurate.

Worked example (length): suppose your true height is exactly $5'9''$. Measuring with a yardstick repeatedly gives $5'0''$ -- consistent (precise) but wrong (not accurate). Measuring with a laser yardstick gives $5'9''$ -- both correct (accurate) and consistent (precise).

Numerical example (resolution vs. accuracy). The true value of a length is near $5.678$ cm. A coarse instrument (resolution $0.1$ cm) reads $5.5$ cm; a finer instrument (resolution $0.01$ cm) reads $5.38$ cm. The first reading is more accurate (closer to $5.678$) but less precise (coarser resolution); the second is less accurate but more precise -- accuracy and precision can pull in opposite directions for the same object. …