Precision - this is how reproducible a measurement is compared to other similar measurements. In other words, the more decimal places you have, the more precise your number is.
Accuracy - this is how close your measurement (or average measurement, in some cases) comes to the accepted/real value
Let's say you're shooting arrows at a target. If you shoot 5 arrows, and they all end up close to the bullseye, but all of them are far apart from each other, then the shots were accurate, but not precise.
If you shoot 5 arrows and they are far away from the bullseye, but are very close together, as if you shot all 5 of them at the same time into the same area, then your shots were very precise.
If your 5 shots were both very close to the bullseye, and very close together (meaning you can hit the same area consistently), then your shots were both very accurate and very precise.
Now:
Realize that no measurements are exact. Every measurement is just a best estimate, meaning there is room for error and "uncertainty".
However, when you count a set of objects, it is exact. There are 5 humans. There can't be 4.34 humans.
Now that we know the background, what is uncertainty?
A: Uncertainty is the margin of error, usually stated by giving a range of values that contains the real or true value.
There are 2 types of uncertainty: Absolute and Relative.
In absolute uncertainty, there are 2 methods.
Method 1: First, discard any unreasonable data first. You must have at least 3 reasonable measurements in order to use this method. Then, take the average of the measurements. Then, find the largest difference between the average and either the lowest or highest reasonable measurement.
For example:
Trial 1 - 15.3 g
Trial 2 - 15.5 g
Trial 3 - 15.2 g
Trial 4 - 11.9 g (remove it, because it looks very different from the rest of the data)
Average of the reasonable measurements: 15.3g
Difference between average and lowest number = 15.3g - 15.2 g = 0.1 g
Difference between average and highest number = 15.5g - 15.3g = 0.2 g
Absolute certainty based on average: 15.3 ± 0.2 g
Method 2: By using the uncertainty of each instrument
Measure to the best precision, then estimate to 0.1 of the smallest segment on instrument scale.
For example, a ruler's smallest segment is 1 mm. The uncertainty would be the tenth of 1 mm, which is 0.1 mm. So the data recorded for a measurement with a ruler would be:
_____(measured value to the best precision) ± 0.1 mm
In relative uncertainty, it is the ratio of absolute uncertainty to the estimated measurement.
So for example, if the data was 39.3 ± 0.1 g, then the relative uncertainty would be 0.1 / 39.3
This can be expressed in percentage, or in Significant Figures.
The number of significant figures is the relative uncertainty. Refer to the previous blog post for info on Significant Figures.
Here's a video
