Monday, November 1, 2010

Accuracy, Precision, and Uncertainty



It is true that we cannot measure things exactly (unless we're robots...) however that doesn't mean we can't give it our best. Here are a few notes we took last class, explaining the uncertainties of measurements.

- Precision: How reproducible a measurement is compared to other similar measurements.
- Accuracy: How close the measurement (or average measurement) comes to the accepted or real value.


Measurement and Uncertainty
- No measurement is exact. Only best estimates which has a some degree of uncertainty.
-Only when we count do we get an exact number (ex: There are 28 students in this class. There cannot be   
 28.5... that would be just weird.)

Absolute Uncertainty
-Uncertainty is expressed in the units of measurement not ratio

Method 1: Make 3 measurements, calculate the average (Make sure to take out the measurements that are "different" from the others. Ex: 2.3, 2.32, 2.46, 2.33). The absolute uncertainty = largest difference between the average and lowest/highest reasonable measurement.

Method 2: Determine the uncertainty of each instrument. Always measure to the best precision that you can. Therefore you should estimate to a fraction 0.1 of the smallest segment on the instrument scale. (On your ruler the smallest division = 1mm. Your best precision should be to break this into 10 equal pieces.)
Relative Uncertainty and Significant Figures
-Relative uncertainty = absolute uncertainty divided by estimated measurement
-Relative uncertainty can be expressed
  • In percent %
  • or using significant figures (sig. figs.)
- The number of sig. figs. = relative uncertainty: The last digit in a measurement is uncertain as it could be one digit higher or lower very easily.

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