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Suppose that you have the task of measuring the lengths of a river and a pipe and come up with 4,999 m and 9 m, respectively. If the true values are 5,000 m and 10 m, respectively, compute (a) the absolute true error and (b) the relative true error for each case. What conclusions can you make regarding the measurements?

Answer :

ngallia

Answer:

(a) [tex]Ae_{river} = 1 m\\[/tex]

[tex]Ae_{pipe} = 1 m\\[/tex]

(b)[tex]Re_{river} = 0.0002\\[/tex]

[tex]Re_{pipe} = 0.1\\[/tex]

Explanation:

By definition,

Absolute Error (Ae) = Actual Value - Measured Value

and Relative Error (Re) = Absolute Error / Actual Value

For the river measurement:

[tex]Ae_{river} = 5000 - 4999 = 1[/tex]

[tex]Re_{river} = 1 / 5000 = 0.0002[/tex]

For the pipe measurement:

[tex]Ae_{pipe} = 10 - 9 = 1[/tex]

[tex]Re_{pipe} = 1 / 10 = 0.1[/tex]

You can conclude that all measurements have the same -1m error, regardless of the length measured. This seems to be a systematic error, caused either by a calibration or zero-offset error on the tool used for measurement, or by an incorrect measurement by the personnel involved.

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