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Random and Systematic Errors

No measurement is perfect. The difference between a measured value and the true value is caused by errors, which come in two kinds.Random errors make repeated readings scatter unpredictably above and below the mean. Causes include small changes in the surroundings, judging a reading by eye, or reaction time that varies from one go to the next. Random errors affect precision. Their effect can be reduced by taking repeat readings and calculating a mean, or by using an instrument with a finer scale or data logging, but they can never be removed completely.Systematic errors shift every reading by the same amount in the same direction. Causes include a zero error (an instrument that does not read zero when it should), an instrument that is wrongly calibrated, or always reading a scale from the same wrong angle. Systematic errors affect accuracy. Repeating readings does not reduce them, because every reading is wrong in the same way. They are reduced by calibrating instruments against a known value, correcting for zero errors and improving the technique.On a graph that should pass through the origin, a systematic error often shows up as a line with a non-zero intercept, while random errors show up as points scattered about the line of best fit.Worked example: a micrometer reads +0.02 mm when its jaws are closed. A wire then gives a reading of 3.47 mm. Every reading is 0.02 mm too large, so the corrected diameter is 3.47 − 0.02 = 3.45 mm.

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Specification: AQA Physics (7407), AS-level, 3.1.2 Limitation of physical measurements. Topic: Measurements and Errors.

Key terms in this lesson

Nucleon
A neutron or a proton; either type of particle found in the nucleus of an atom.

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