Accuracy and Precision

Precision is how reproducible a measurement is compared to other similar measurements.
Accuracy is how close the measurement (or average measurement) comes to the accepted or real measurement.
Uncertainty is the margin of error and there are two types of uncertainty, absolute and relative.

There are 2 methods of finding absolute uncertainty

Method 1: Discard any unreasonable information.  Then find the average of the 3 numbers and find the largest difference between the average and either the lowest or highest reasonable measurement.

Trial 1 - 29.86 g (this would be discarded because the other numbers include numbers from 0.90-0.96)
Trial 2 - 29.97 g
Trial 3 - 29.93 g
Trial 4 - 29.94 g
Trial 5 - 29.96 g
Average of the numbers: 29.95 g

Difference between average and lowest number =  29.95g - 29.93g = 0.02g
Difference between average and highest number = 29.97g - 29.95g = 0.02g
Absolute certainty based on average: 29.95 ± 0.2 g

Method 2: Measure to the most precise measurement then estimate to the 0.1 of the smallest measurement on a measuring instrument. 

For example, if the measuring instrument is a ruler, the smallest measurement is 0.1mm.  The data recorded for a measurement of a ruler would end up looking  like  ________(best precise measurement) ±0.1mm
For relative uncertainty, it is the ratio of absolute uncertainty to the estimated measurement. For example, if the absolute uncertainty is 29.95 ± 0.2 g, the relative uncertainty would be 0.2 / 29.95.  It can be expressed as a percentage or in significant figures. 

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