If you are conducting an important experiment, you want measurement tools that are accurate and precise. Accuracy refers to how close an individual measurement is to a known standard. For example, if you use a balance to mass an object you know is 10 grams, an accurate balance should read 10 grams or very close to it. Precision is how close two or more measurements are to one another. A precise balance should give very similar readings if used to mass the same object several times. Repeatability is like precision -- a number that reflects the similarity or closeness of several measurements of the same object made by the same tool. Repeatability is defined as the standard deviation of the individual measurements.

Suppose you want to determine the repeatability of your balance's measurement of a 10-gram object. You use the balance to mass the object five times and get the following measurements in grams:

9.8, 10.1, 9.5, 10.2, 10.4

The first step in calculating repeatability is to find the average, or mean, of the measurements. To do this, add all the measurements together and divide the sum by the number of measurements.

(9.8 + 10.1 + 9.5 + 10.2 + 10.4) ÷ 5 = 10

Find the differences between the average and each individual measurement and square each difference.

(9.8 - 10)^2 = 0.04 (10.1 - 10)^2 = 0.01 (9.5 - 10)^2 = 0.25 (10.2 - 10)^2 = 0.04 (10.4 - 10)^2 = 0.16

Add the squared differences together and divide the sum by one less than the number of measurements.

(0.04 + 0.01 + 0.25 + 0.04 + 0.16) ÷ 4 = 0.125

Finally, find the square root of the previous answer.

square root (0.125) = 0.35

The repeatability of your measurements is 0.35. This means that, using this particular balance, you can expect the majority of measurements of a 10-gram object to be within 0.35 grams of the actual mass.