errors

Errors are deviations of observed values from true values, intended outcomes, or expected results. They arise in many fields, including science, engineering, statistics, and computing, and are often addressed through measurement, analysis, and error management. Distinguishing between error and mistake is important: error typically denotes a discrepancy that can be quantified or reduced, whereas a mistake implies a preventable wrong action.

Types of errors commonly discussed include random (or stochastic) errors, systematic errors, and gross errors. Random errors vary unpredictably and tend to average out with repeated measurements. Systematic errors introduce consistent bias due to flawed equipment, procedures, or assumptions and are harder to detect. Gross errors result from mistakes in data collection, recording, or processing. In statistics and measurement, errors are accompanied by uncertainty, which is quantified using indicators such as standard deviation, standard error, confidence intervals, and error bars.

Error analysis seeks to identify sources, estimate magnitude, and minimize impact. Practices include calibration against standards, replication of measurements, control of environmental conditions, and method validation. Error propagation studies how individual uncertainties combine to affect derived results, often using linear approximation or stochastic simulation.

In computing and data processing, an error refers to an abnormal condition that disrupts normal operation. Programs implement error handling to detect, report, and recover from errors, using mechanisms such as error codes, exceptions, and fallback procedures. In predictive modeling, residuals measure discrepancy between observed and predicted values and inform model refinement.

Overall, understanding errors involves quantifying uncertainty, identifying sources, and applying strategies to reduce bias and improve reliability.