Random Error

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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