1.3 Accuracy, Precision & Errors

In science, accuracy and precision have very specific meanings.

• Accuracy: How close a measurement is to the true, accepted value, for example gravity has a true value of 9.81m/s to 3 s.f.
• Precision: How close your repeated measurements are to each other. High precision means your results are very repeatable, even if they are wrong.

The best way to remember this is with a target analogy.

In an experiment, you are "accurate" if your average result is near the true value. You are "precise" if all your results are tightly clustered together.

An error is the difference between your measured value and the true value. There are two main types of error you need to know.

Systematic Errors

A systematic error is a repeating error that affects all your measurements in the same way (e.g., they are all 0.2 cm too high).

• Cause: Usually caused by faulty equipment (a "zero error," like a scale that reads 0.1 kg before you put anything on it) or a flawed method.
• Effect: It reduces the accuracy of your results.
• Fix: Cannot be fixed by repeating. You must fix the equipment or method (e.g., subtract the 0.1 kg "zero error" from all your readings).

This graph shows ideal measurements with systematic uncertainty in the values. The uncertainty is represented by the solid lines through each value.

Random Errors

A random error is an unpredictable error that causes your measurements to be scattered around the true value.

• Cause: Usually caused by human error (like different reaction times when using a stopwatch) or by reading an instrument (like judging the exact value between two lines on a ruler).
• Effect: It reduces the precision of your results.
• Fix: You can reduce the effect of random errors by taking multiple readings and calculating an average (mean).