# Random Error

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Random errors are unavoidable. They are unavoidable due to the fact that every physical measurement has limitation, i.e., some uncertainty.
Using the utmost of care, the analyst can only obtain a weight to the uncertainty of the balance or deliver a volume to the uncertainty of the glass pipette.
For example, most four-place analytical balances are accurate to $\pm 0.0001$ grams. Therefore, with care, an analyst can measure a $1.0000$ gram weight (true value) to an accuracy of $\pm 0.0001$ grams where a value of $1.0001$ to $0.999$ grams would be within the random error of measurement. If the analyst touches the weight with their finger and obtains a weight of $1.0005$ grams, the total $$\text{error} = 1.0005 -1.0000 = 0.0005 \text{ grams}$$ and the random and systematic errors could be estimated to be $0.0001$ and $0.0004$ grams respectively. Note that the systematic error could be as great as $0.0006$ grams, taking into account the uncertainty of the measurement.
A truly random error is just as likely to be positive as negative, making the average of several measurements more reliable than any single measurement.
Hence, taking several measurements of the $1.0000$ gram weight with the added weight of the fingerprint, the analyst would eventually report the weight of the finger print as $0.0005$ grams where the random error is still $0.0001$ grams and the systematic error is $0.0005$ grams. However, random errors set a limit upon accuracy no matter how many replicates are made.

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