systematic and random errors

When a measurement misses the true value, the miss comes in two flavours. A random error pushes your reading up or down unpredictably each time: noise, a slightly different reaction time, tiny draughts. A systematic error pushes every reading the same way: a ruler that starts at 1 mm instead of 0, a stopwatch that runs slow, a scale not zeroed. Telling them apart is the first step to a trustworthy result.

Random errors scatter symmetrically about the true value, so they largely cancel if you average many trials; their size sets your precision, and taking N readings shrinks the uncertainty of the mean by a factor of sqrt(N). Systematic errors do not cancel by averaging; they bias every reading in the same direction, so they set your accuracy and can only be removed by finding the cause (calibrating the instrument, correcting the zero, controlling the condition).

This maps directly onto precision and accuracy: random error limits precision, systematic error limits accuracy. A good experimenter attacks both, repeating to beat down random error and calibrating and cross-checking to hunt down systematic error.