Uncertainty and error in measurement. Error Uncertainty in a measurement Limit to the precision or accuracy Limit to the reliability An error is not a.

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Presentation transcript:

Uncertainty and error in measurement

Error Uncertainty in a measurement Limit to the precision or accuracy Limit to the reliability An error is not a mistake.

Two main types of Errors Random errors Systematic errors.

Random Errors Uncertainty because we never read a measurement exactly Individual values vary about the average or mean.

Random Errors Random errors may be detected by repeating the measurements Random errors can be reduced by repeating the measurements The average of more and more readings will approach more closely the true value.

Examples of Random Errors Measuring the Length of a table several times will give slightly different results Different measurements of Force will be taken when finding the weight of an object.

Random Errors and Precision A result is precise if it is relatively free from random error Precise if the random error is small.

Systematic Errors Error due to the fact that no instrument or method is perfect Repeated measurements with the same apparatus will not show systematic error Repeated measurements with the same apparatus will not eliminate systematic error.

Examples of Systematic Errors Instrument zero errors Variations in spacing of graduations on a scale Deflections not quite proportional to the force e.g. ammeter.

Systematic Errors and Accuracy A result is accurate if it is relatively free from systematic error Accurate if the systematic error is small.

And… If large random errors are present, they will show up in a large value for the final quoted error Everyone is aware of the inaccuracy of the result The concealed presence of a systematic error may lead to an apparently reliable result, with a small estimated error, which is in fact seriously wrong.

Finally… A measurement may be very precise (high precision) but very inaccurate (low accuracy) due to zero offset error High precision means low random error Low precision means high random error Low accuracy means high systematic error High accuracy means low systematic error.