# Accuracy

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Accuracy refers to the closeness of a measured value to a standard or known value.
For example: if in a lab you obtain a weight measurement of 3.2 kg for a given substance, but the actual or known weight is 10 kg, then your measurement is not accurate. In this case, your measurement is not close to the known value. If your resulted value are close to $10kg$, e.g ($9kg$ or $11kg$) then we can say that your measurement is accurate to $\pm 1kg$.
In analytical chemistry, the term 'accuracy' is used in relation to a chemical measurement. The International Vocabulary of Basic and General Terms in Metrology (VIM) defines accuracy of measurement as... "closeness of the agreement between the result of a measurement and a true value." The VIM reminds us that accuracy is a "qualitative concept" and that a true value is indeterminate by nature.
In theory, a true value is that value that would be obtained by a perfect measurement. Since there is no perfect measurement in analytical chemistry, we can never know the true value.
Our inability to perform perfect measurements and thereby determine true values does not mean that we have to give up the concept of accuracy. However, we must add the reality of error to our understanding. For example, lets call a measurement we make $X_I$ and give the symbol $\mu$ for the true value. We can then define the error in relation to the true value and the measured value according to the following equation: $$\text{error} = X_I - \mu \tag{1}$$ We often speak of accuracy in qualitative terms such a "good," "expected," "poor," and so on. However, we have the ability to make quantitative measurements. We therefore have the ability to make quantitative estimates of the error of a given measurement. Since we can estimate the error, we can also estimate the accuracy of a measurement. In addition, we can define error as the difference between the measured result and the true value as shown in eq. 1 above.
However, we cannot use eq. 1 to calculate the exact error because we can never determine the true value. We can, however, estimate the error with the introduction of the 'conventional true value' which is more appropriately called either the assigned value, the best estimate of a true value, the conventional value, or the reference value. Therefore, the error can be estimated using equation 1 and the conventional true value.
Errors in analytical chemistry are classified as systematic (determinate) and random (indeterminate). The VIM definitions of error, systematic error, and random error follow:
Error - the result of a measurement minus a true value of the measurand.
Systematic Error - the mean that would result from an infinite number of measurements of the same measurand carried out under repeatability conditions, minus a true value of the measurand.
Random Error - the result of a measurement minus the mean that would result from an infinite number of measurements of the same measurand carried out under repeatability conditions.

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