Question

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 1

(a)
`Ae_(river) = 1 m\\`

`Ae_(pipe) = 1 m\\`

(b)
`Re_(river) = 0.0002\\`

`Re_(pipe) = 0.1\\`

Step-by-step explanation:

By definition,

Absolute Error (Ae) = Actual Value - Measured Value

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

For the river measurement:

`Ae_(river) = 5000 - 4999 = 1`

`Re_(river) = 1 / 5000 = 0.0002`

For the pipe measurement:

`Ae_(pipe) = 10 - 9 = 1`

`Re_(pipe) = 1 / 10 = 0.1`

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.