How to Calculate Precision

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Precision is how close a measurement comes to another measurement. If using a particular tool or method achieves similar results every time it is used, it has high precision, such as stepping on a scale several times in a row and getting the same weight every time. You can calculate precision using different methods, including range of values and average deviation.

TL;DR (Too Long; Didn't Read)

Precision is not the same as accuracy. Precision is how close measured values are to each other, and accuracy is how close experimental values come to the true value. Data may be accurate but not precise, or precise but not accurate.

Range of Values

    Work out the highest measured value and lowest measured value by sorting your data in numerical order, from lowest to highest. If your values are 2, 5, 4 and 3, sort them as 2, 3, 4 and 5. You can see that the highest measurement is 5, and the lowest measured value is 2.

    Work out 5 − 2 = 3. (In this example, your highest value is 5 and your lowest value is 2.)

    Report the result as the mean, plus or minus the range. While you don't work out the mean in this method, it's standard to include the mean when reporting a precision result. The mean is simply the sum of all the values, divided by the number of values. In this example, you have four measurements: 2, 3, 4 and 5. The mean of these values is:

    \frac{2+3+4+5}{4} = 3.5

    You report the result as 3.5 ± 3 or mean = 3.5, range = 3.

Average Deviation

    Calculate the mean of the measured values, i.e. the sum of the values, divided by the number of values. If you use the same example as above, you have four measurements: 2, 3, 4 and 5. The mean of these values is:

    \frac{2+3+4+5}{4} = 3.5

    Calculate the absolute deviation of each value from the mean. You need to establish how close each value is to the mean. Subtract the mean from each value. It doesn't matter if the value is above or below the mean, simply use the positive value of the result. In this example, the absolute deviations are 1.5 (2 − 3.5), 0.5 (3 − 3.5), 0.5 (4 − 3.5) and 1.5 (5 − 3.5).

    Add the absolute deviations together to find their mean using the same method you used to find the mean. Add them together, and divide by the number of values. In this example, the average deviation is:

    \frac{1.5+0.5+0.5+1.5}{4} = 1

    Report the result as the mean, plus or minus the average deviation. In this example, the result is 3.5 ± 1. You could also say: mean = 3.5, range = 1.

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