Using repeated measurements to improve the standard uncertainty
Content
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 Traceability 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.
Availability
- View the leaflet in Bulgarian (pdf, 134 kB) (new window)
- View the leaflet in Czech (pdf, 184 kB) (new window)
- View the leaflet in English (pdf, 111 kB) (new window)
- View the leaflet in Estonian (pdf, 158 kB) (new window)
- View the leaflet in German (pdf, 126 kB) (new window)
- View the leaflet in Greek (pdf, 146 kB) (new window)
- View the leaflet in Spanish* (pdf, 260 kB) (new window)
- View the leaflet in Turkish (pdf, 150 kB) (new window)
- View the leaflet in Ukrainian* (pdf, 180 kB) (new window)
*2015 edition
Translation
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.
This information leaflet is intended for laboratories perfoming chemical analyses. It has been prepared by the Eurachem 
EURACHEM through its