Using repeated measurements to improve the standard uncertainty


Analysts often take multiple observations, and sometimes average the result of several observations to reduce the uncertainty associated with random variation. However, it is often unclear how the standard uncertainty associated with averaged results should be calculated from an observed standard deviation. Sometimes one should divide by the square root of the number of observations; sometimes the standard deviation is used unchanged, and sometimes some alternative formula is appropriate. 

This information leaflet has been prepared by the Eurachem Measurement Uncertainty and Tracability Working Group (see here for details) to give further explanation of when the classical 'root n' formula can, and can not, be used. The leaflet amplifies principles described in the Eurachem Guide "Quantifying uncertainty in analytical measurement", which is available here.



*2015 edition


Translation into other languages is encouraged for members of Eurachem. Other offers of translation should be directed to the Eurachem Secretariat for permission. The Eurachem policy on maintenance and development of Eurachem guidance, available on the Policies page, gives further information on translation.

Amendment history

This leaflet was amended to improve clarity in April 2016. The previous English version, as issued in 2015, is available for comparison.