Uncertainty and error in measurement

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Uncertainty and error in measurement
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Error

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

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Two main types of Errors

• Random errors
• Systematic errors.

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Random Errors

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

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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.

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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.

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Random Errors and Precision

• A result is precise if it is relatively free from
  random error
• Precise if the random error is small.

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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.

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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.

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Systematic Errors and Accuracy

• A result is accurate if it is relatively free
  from systematic error
• Accurate if the systematic error is small.

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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.

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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.