keskivirhe

Keskivirhe, or mean error, is a term used in statistics and metrology to describe the average signed deviation of observed values from a known true value across multiple measurements or trials. It is defined as E[e] = (1/n) ∑ (x_i - t), where x_i are measured values and t is the true value. If the quantity being measured is estimated from data, the keskirhe of the estimator corresponds to the bias of the estimator, i.e., E[μ_hat - μ].

The keskirhe reflects systematic error: a nonzero average deviation indicating a consistent offset in the measurement process. If the keskirhe is zero, the process is unbiased on average. It is important to distinguish keskirhe from other error measures such as the mean absolute error (MAE) or the root mean square error (RMSE), which quantify overall accuracy without canceling positive and negative deviations. A small keskirhe does not guarantee small MAE or RMSE, since large individual errors can offset each other.

Practical use cases include instrument calibration, quality control, and evaluating measurement procedures. A known true value or a reference standard is required to compute keskirhe; when the true value is unknown, one can compare to a reference or use repeated measurements to estimate the bias.

In Finnish statistical language, keskirhe is often discussed alongside concepts like bias (systematic error) and random error (satunnaisvirhe). It serves as a basic indicator of whether a measurement system tends to over- or under-estimate a quantity on average.