Coursework Averages

Here are three extension readings in mm: 30, 31, 31.

According to our calculator, the average extension is 30·66666667 mm. However: this implies we're able to measure extensions to a hundred-millionth of a millimetre!

With a ruler this is not possible!

Instead we must make sure that the average result is recorded to the same degree of precision as the original data: in this case to the nearest mm.

The average of 30, 31 and 31 is 31 mm (to the nearest mm).

Say we had measured the extension with a more accurate device (such as a vernier scale - ask your teacher to show you one!). We could have recorded these results instead:

30·2, 30·9, 31·4

Here is their average... 30·83333333

Again, we must ensure our final average is only as accurate as the original data, in this case to the nearest tenth of a millimetre: 30·8 mm.

Notice that if we were to round this up to the nearest millimetre (like our original results) we end up with the same answer: 31 mm. We do not end up with what our calculator first claimed.