Uncertainty and error in measurement Error Uncertainty in

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.