||It has been suggested that this article be merged with Random and systematic errors. (Discuss) Proposed since February 2013.|
Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measures of a constant attribute or quantity are taken. The word random indicates that they are inherently unpredictable, and have null expected value, namely, they are scattered about the true value, and tend to have null arithmetic mean when a measurement is repeated several times with the same instrument. All measurements are prone to random error.
Random error is caused by unpredictable fluctuations in the readings of a measurement apparatus, or in the experimenter's interpretation of the instrumental reading; these fluctuations may be in part due to interference of the environment with the measurement process.
The concept of random error is closely related to the concept of precision. The higher the precision of a measurement instrument, the smaller the variability (standard deviation) of the fluctuations in its readings.
Systematic versus random error 
Random error is always present in a measurement. It is caused by inherently unpredictable fluctuations in the readings of a measurement apparatus or in the experimenter's interpretation of the instrumental reading.
Whereas, systematic errors are predictable, and typically constant or proportional to the true value. If the cause of the systematic error can be identified, then it can usually be eliminated. Systematic errors are caused by imperfect calibration of measurement instruments or imperfect methods of observation, or interference of the environment with the measurement process, and always affect the results of an experiment in a predictable direction. Incorrect zeroing of an instrument leading to a zero error is an example of systematic error in instrumentation.
The Performance Test Standard PTC 19.1-2005 “Test Uncertainty”, published by the American Society of Mechanical Engineers (ASME), discusses systematic and random errors in considerable detail. In fact, it conceptualizes its basic uncertainty categories in these terms.
See also 
- John Robert Taylor (1999). An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. University Science Books. p. 94, §4.1. ISBN 0-935702-75-X.