Editing Analytical chemistry (section)

== Errors ==
{{Main|Approximation error}}
Error can be defined as numerical difference between observed value and true value.<ref>G.L. David - ''Analytical Chemistry''</ref> The experimental error can be divided into two types, systematic error and random error. Systematic error results from a flaw in equipment or the design of an experiment while random error results from uncontrolled or uncontrollable variables in the experiment.<ref>{{Cite book |last1=Harris |first1=Daniel C. |url=https://www.worldcat.org/oclc/915084423 |title=Quantitative chemical analysis |last2=Lucy |first2=Charles A. |date=29 May 2015 |publisher=W.H. Freeman |isbn=978-1-4641-3538-5 |edition=9th |location=New York |oclc=915084423}}</ref>

In error the true value and observed value in chemical analysis can be related with each other by the equation
: <math> \varepsilon_{\rm a} = |x - \bar{x}| </math>
where
* <math>\varepsilon_{\rm a}</math> is the absolute error.
* <math>x</math> is the true value.
* <math>\bar{x}</math> is the observed value.
An error of a measurement is an inverse measure of accurate measurement, i.e. smaller the error greater the accuracy of the measurement.

Errors can be expressed relatively. Given the relative error(<math>\varepsilon_{\rm r}</math>):
: <math>\varepsilon_{\rm r} = \frac{\varepsilon_{\rm a}}{|x|} = \left | \frac{x - \bar{x}}{x} \right |</math>

The percent error can also be calculated:
: <math>\varepsilon_{\rm r} \times 100\% </math>

If we want to use these values in a function, we may also want to calculate the error of the function. Let <math>f</math> be a function with <math>N</math> variables. Therefore, the [[propagation of uncertainty]] must be calculated in order to know the error in <math>f</math>:
: <math>\varepsilon_{\rm a} (f) \approx  \sum_{i = 1}^N \left | \frac{\partial f}{\partial x_i} \right | \varepsilon_{\rm a}(x_i) = \left | \frac{\partial f}{\partial x_1} \right | \varepsilon_{\rm a}(x_1) + \left | \frac{\partial f}{\partial x_2} \right | \varepsilon_{\rm a}(x_2) + \ldots + \left | \frac{\partial f}{\partial x_N} \right | \varepsilon_{\rm a}(x_N)</math>