Fractional Uncertainty and Precision/Accuracy

[ntox101]

Homework Statement

I am to use a stopwatch and record the time is takes for me to start and stop it ten times. I have collected my data, and calculated the average along with uncertainty and a fractional uncertainty. I am asked if the fractional uncertainty is a measure of precision or accuracy? I am not quite sure.

Homework Equations

The Attempt at a Solution

I believe that the fractional uncertainty is related to accuracy because no matter how many times I start and stop the watch, it is going to be around the same value each time. The (.06s) / (.18s) uncertainty which is .33, is referring to how accurate I am to my average value.

I know the different between precision and accuracy. For example a dartboard. All shots in the bullseye, close to each other represents both. Shots bunched together but not close to the bullseye would represent precision. How does this relate to this stopwatch experience?


Any feedback much appreciated.

Thanks

 

[anathema]

for your post and for sharing your data! The fractional uncertainty in this case is indeed a measure of accuracy, as it represents the deviation of your individual measurements from the average. This is similar to your example of the dartboard, where shots close to the bullseye represent both precision and accuracy, while shots bunched together but not close to the bullseye represent precision without accuracy. In the case of the stopwatch, the smaller the fractional uncertainty, the more accurate your measurements are compared to the average. Keep up the good work with your experiments and data collection!

 

[tomcue]

for your question. You are correct in thinking that the fractional uncertainty is related to accuracy. In this case, the fractional uncertainty is a measure of how close your measurements are to the true or expected value. In other words, it is a measure of how accurate your measurements are.

Precision, on the other hand, refers to the consistency or repeatability of your measurements. In the dartboard example, all shots in the bullseye would represent both precision and accuracy, as they are both close to the center and consistent with each other. Shots bunched together but not close to the bullseye would represent precision, as they are consistent with each other but not accurate.

In the case of the stopwatch, if your measurements are all close to the average value and consistent with each other, then you have both precision and accuracy. However, if your measurements are close to the average value but not consistent with each other, then you have accuracy but not precision. And if your measurements are not close to the average value, then you have neither precision nor accuracy.

I hope this helps clarify the difference between precision and accuracy in this context. Keep in mind that both precision and accuracy are important in scientific measurements, as they contribute to the overall reliability and validity of your data.