To determine the uncertainty of a measurement "by hand":
Make the same measurement multiple times.
Find the mean of the measurement. And then report one of these (as you go down the list, these increase in sophistication) :
"approximate uncertainty": the maximum difference of the measurement from the mean . This is the easy way out, as it requires very little calculation. Just find the number that is the "farthest away" from the mean, subtract the two numbers, and report the result as the approximate uncertainty. Useful for discussion, but not appropriate for a formal lab.
average uncertainty (see average deviation): the average difference from the mean, perhaps a little more useful than the approximate uncertainty. Find the average. Subtract the individual measurements from the average. Take the absolute value of each difference (ignore negative answers). Average the differences. Report the result as the average uncertainty. This is the minimum you should be doing for lab reports.
percentage uncertainty: find the percentage of the measurement that the average uncertainty represents. See the link for an example. This one is also appropriate for our lab reports.
standard deviation: more time consuming, but gives a better picture of your measurement. See the link for an example.
To make Logger Pro calculate your uncertainty or "standard error":
Insert a curve fit or linear fit.
Double-click on the box displaying the equation for the best-fit.
Select "Show Uncertainty" or "Show Standard Error".
Logger Pro will display a standard deviation (even though it says "uncertainty" or "standard error") for each value in the box showing the curve fit.
For more information:
See attached document (below) for a more complete discussion of uncertainty. For paradigm lab reports, a mention of the range of differences from the average value is sufficient. Vernier Software & Technology makes most of the computer-based lab equipment we use. They have this to say about the uncertainty of their measurement tools.
Approximate range from ± 0.4 to ±0.1 s, depending on type of event
Pasco and Vernier Rotary Motion Sensors (slightly different in appearance)
Note: both have 10 mm, 29 mm, and 48 mm diameter pulleys.
± 0.09 deg (minimum)
Dual-Range Force Sensor
± 10 N Range: 0.01 N
(minimum) ± 50 N Range: 0.05 N (minimum)
Motion Sensor/Motion Detector
± 0.001 m (minimum)
Gas Pressure Sensor
typical ±0.25% full scale (minimum)
typically ±0.0005 m to ±0.001 m depending on measurement
Differential Voltage Probe
estimated +/- 0.1 V (can be improved with calibration)