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Accuracy and Precision

Key Concepts

  • Accuracy describes the agreement between the determined value and the true value.
    The opposite of accurate is inaccurate.

  • An accurate measurement has a very low percentage relative error.

  • Precision describes the reproducibility of a measurement.
    The opposite of precise is imprecise.

  • Precise measurements have a very narrow range of values.

  • Measurements can be described as:

    • accurate and precise

    • accurate but imprecise

    • inaccurate but precise

    • inaccurate and imprecise

Accuracy

Accuracy describes the agreement between the determined value and the true value.

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When talking about the accuracy of a measurement, Chemists like to know just how accurate the measurement is.
For this reason, we calculate the percentage relative error as shown below:

percentage relative error = true value - determined value
true value
x 100

For an accurate measurement, the pecentage relative error will be very low, close to 0 %
For an inaccurate measurement, the percentage relative error will be high, for example, greater than 5 %.

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If we know the tolerance of a true measurement, we can decide that the determined value is accurate if it lies within the tolerance levels of the true measurement, and, inaccurate if it lies outside the tolerance levels of the true value.

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In order to determine how accurate a measurement is, we need to know the true value.
Often we don't know the true value, so we can't determine how accurate our results are.

Precision

Because it is very rare for Chemists to know how accurate a measurement is, they make a number of measurements under the same conditions until they arrive at a set of measurements that are in good agreement with each other.

The reproducibility of a measurement is known as precision.
When all the measurements are very similar, we say the determined value is known precisely.
If we cannot get measurements that are very similar, we cannot say the value is known precisely, instead we say the measurements are imprecise.

We can make generalisations about the precision of a set of measurements by calculating the range of the experimentally determined values:

range of values = largest value - smallest value

A set of measurements can be described as precise if the range of values is very small, that is, range is close to 0
A set of measurements will be described as imprecise if the range of values is large, that is, range is not close to 0.

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Examples of Accuracy and Precision

Accuracy describes the agreement between the determined value and the true value.
Precision describes the reproducibility of a measurement.

Therefore measurements can be described as one of the following:

  • accurate and precise

  • accurate but imprecise

  • inaccurate but precise

  • inaccurate and imprecise

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