Editing Standard deviation (section)

====Experiment, industrial and hypothesis testing====
Standard deviation is often used to compare real-world data against a model to test the model.
For example, in industrial applications the weight of products coming off a production line may need to comply with a legally required value. By weighing some fraction of the products an average weight can be found, which will always be slightly different from the long-term average. By using standard deviations, a minimum and maximum value can be calculated that the averaged weight will be within some very high percentage of the time (99.9% or more). If it falls outside the range then the production process may need to be corrected. Statistical tests such as these are particularly important when the testing is relatively expensive. For example, if the product needs to be opened and drained and weighed, or if the product was otherwise used up by the test.

In experimental science, a theoretical model of reality is used. [[Particle physics]] conventionally uses a standard of "'''5 sigma'''" for the declaration of a discovery. A five-sigma level translates to one chance in 3.5 million that a random fluctuation would yield the result. This level of certainty was required in order to assert that a particle consistent with the [[Higgs boson]] had been discovered in two independent experiments at [[CERN]],<ref>{{cite web |url=http://press-archive.web.cern.ch/press-archive/PressReleases/Releases2012/PR17.12E.html |title=CERN experiments observe particle consistent with long-sought Higgs boson &#124; CERN press office |publisher=Press.web.cern.ch |date=4 July 2012 |access-date=30 May 2015 |archive-date=25 March 2016 |archive-url=https://web.archive.org/web/20160325050100/http://press-archive.web.cern.ch/press-archive/PressReleases/Releases2012/PR17.12E.html |url-status=dead }}</ref> also leading to the declaration of the [[first observation of gravitational waves]].<ref>{{Citation|vauthors=((LIGO Scientific Collaboration)), ((Virgo Collaboration))|title=Observation of Gravitational Waves from a Binary Black Hole Merger|journal=Physical Review Letters|volume=116|issue=6|year=2016|pages=061102|doi=10.1103/PhysRevLett.116.061102|arxiv=1602.03837|pmid=26918975|bibcode=2016PhRvL.116f1102A|s2cid=124959784}}</ref>