How to find the precision and absolute error of a measurement - Example 2
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An example looking at the relationship between precision and absolute error. Recall that the precision of a measuring instrument is the smallest unit it can measure, for example the precision of a millimetre ruler will be 1 mm. The absolute error would therefore be +/- half the precision which is +/- 0.5mm.
Always remember that no measuring instrument is 100% accurate. There will always be some "leeway". The actual measurement could be slightly over or under what the reading on the measuring instrument is but we take the closest reading within +/- (give or take) the absolute error.
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Another explanation on how to calculate absolute error, relative error and percentage error is as follows:
You can calculate the absolute error using the resolution (smallest unit of measurement aka precision), relative error, and percentage error as follows:
1. Resolution/Precision (R): The resolution is the smallest unit of measurement that the instrument can detect or display. It represents the precision of the instrument. Let's denote it as "R."
2. Relative Error (RE): Relative error is expressed as a fraction or ratio of the true value, and it represents the fractional difference between the measured value and the true value. Let's denote it as "RE."
3. Percentage Error (PE): Percentage error is the relative error expressed as a percentage, making it more intuitive for communication. Let's denote it as "PE."
Now, to find the absolute error (AE) based on resolution (R), relative error (RE), and percentage error (PE), you can use the following formulas:
1. Absolute Error (AE) based on Resolution (R):
Absolute Error = Resolution / 2
This formula assumes that the actual error can be as much as half the resolution in either direction. It's a common method for estimating the maximum absolute error based on the instrument's resolution.
2. Absolute Error (AE) based on Relative Error (RE):
Absolute Error = |Relative Error| * True Value
In this case, you'll need the true value to calculate the absolute error from the relative error.
3. Absolute Error (AE) based on Percentage Error (PE):
Absolute Error = (Percentage Error / 100) * True Value
Just like with relative error, you need the true value to calculate the absolute error from the percentage error.
Remember that in these calculations, you'll typically have the true value available. If you're working with percentage error, it can be derived from the relative error using the formula PE = |RE| * 100.
The choice of which formula to use depends on the information available to you and how you want to express the error. In practice, it's common to calculate and report absolute error based on resolution if you're concerned about the instrument's precision, and absolute error based on relative or percentage error if you're evaluating the accuracy of measurements.
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