How to calculate standard deviation using equation?
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OverviewThere are certain basic concepts in analytical chemistry that are helpful to the analyst when treating analytical data. This section will address accuracy, precision, mean, and deviation as related to chemical measurements in the general field of analytical chemistry.AccuracyIn analytical chemistry, the term 'accuracy' is used in relation to a chemical measurement. The International Vocabulary of Basic and General Terms in Metrology (VIM) definesaccuracy of measurementas... "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 atrue valueis indeterminate by nature. In theory, atrue valueis that value that would be obtained by a perfect measurement. Since there is no perfect measurement in analytical chemistry, we can never know thetrue value.Our inability to perform perfect measurements and thereby determinetrue valuesdoes not meanthat we have to give up the concept of accuracy. However, we must add the reality oferrorto our understanding. For example, lets call a measurement we make XIand give the symbol µ for thetrue value. We can then define theerrorin relation to thetrue valueand the measured value according to the following equation:error = XI- µ (14.1)We often speak of accuracy in qualitative terms such a "good," "expected," "poor," and so on. However, we have the ability to make quantitativemeasurements. 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 thetrue valueas shown in equation 14.1 above. However, we cannot use equation 14.1 to calculate theexact errorbecause we can never determine thetrue 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 14.1 and theconventional true value.Errors in analytical chemistry are classified assystematic(determinate) andrandom(indeterminate). The VIM definitions oferror, systematic error,andrandom errorfollow:
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