Abstract The geochemical analysis of elemental concentrations and isotopic compositions has to deal with measurement errors all the time. Here, an overview of random, systematic, and gross errors and treatment of random errors using statistical method are presented. Standard deviation is a simple but the most important concept in error analysis. Normal/Gaussian distribution and Poisson distribution and the standard deviations related to these two probability distributions are reviewed. The use of standard deviations to determine the limit of detection and limit of quantification during instrument analysis is highlighted. In the end, an overview of propagation of random errors and systematic errors is provided.