Editing Coefficient of variation (section)

==Definition==
The coefficient of variation (CV) is defined as the ratio of the standard deviation <math>\sigma</math> to the mean <math>\mu</math>, <math>CV = \frac{\sigma}{\mu}.</math><ref>{{cite book|url=https://archive.org/details/cambridgediction00ever_0|title=The Cambridge Dictionary of Statistics|last=Everitt|first=Brian|publisher=Cambridge University Press|year=1998|isbn=978-0521593465|location=Cambridge, UK New York|url-access=registration}}</ref>

It shows the extent of variability in relation to the mean of the population.
The coefficient of variation should be computed only for data measured on scales that have a meaningful zero ([[ratio scale]]) and hence allow relative comparison of two measurements (i.e., division of one measurement by the other). The coefficient of variation may not have any meaning for data on an [[interval scale]].<ref>{{cite web | url=http://www.graphpad.com/faq/viewfaq.cfm?faq=1089 | title=What is the difference between ordinal, interval and ratio variables? Why should I care? | access-date=22 February 2008 | publisher=GraphPad Software Inc | url-status=live | archive-url=https://web.archive.org/web/20081215175508/http://graphpad.com/faq/viewfaq.cfm?faq=1089 | archive-date=15 December 2008 | df=dmy-all }}</ref> For example, most temperature scales (e.g., Celsius, Fahrenheit etc.) are interval scales with arbitrary zeros, so the computed coefficient of variation would be different depending on the scale used. On the other hand,  [[Kelvin]] temperature has a meaningful zero, the complete absence of thermal energy, and thus is a ratio scale. In plain language, it is meaningful to say that 20 Kelvin is twice as hot as 10 Kelvin, but only in this scale with a true absolute zero. While a standard deviation (SD) can be measured in Kelvin, Celsius, or Fahrenheit, the value computed is only applicable to that scale. Only the Kelvin scale can be used to compute a valid coefficient of variability.

Measurements that are [[log-normal]]ly distributed exhibit stationary CV; in contrast, SD varies depending upon the expected value of measurements.

A more robust possibility is the [[quartile coefficient of dispersion]], half the [[interquartile range]] <math> {(Q_3 - Q_1)/2} </math> divided by the average of the quartiles (the [[midhinge]]), <math> {(Q_1 + Q_3)/2} </math>.

In most cases, a CV is computed for a single independent variable (e.g., a single factory product) with numerous, repeated measures of a dependent variable (e.g., error in the production process). However, data that are linear or even logarithmically non-linear and include a continuous range for the independent variable with sparse measurements across each value (e.g., scatter-plot) may be amenable to single CV calculation using a [[Maximum likelihood estimation|maximum-likelihood estimation]] approach.<ref>{{Cite journal|last1=Odic|first1=Darko|last2=Im|first2=Hee Yeon|last3=Eisinger|first3=Robert|last4=Ly|first4=Ryan|last5=Halberda|first5=Justin|date=June 2016|title=PsiMLE: A maximum-likelihood estimation approach to estimating psychophysical scaling and variability more reliably, efficiently, and flexibly|journal=Behavior Research Methods|volume=48|issue=2|pages=445–462|doi=10.3758/s13428-015-0600-5|issn=1554-3528|pmid=25987306|doi-access=free}}</ref>