I'm doing a bio lab, and I have collected data on heart rate measured in beats/15 secs with an uncertainty of +/- 1 beat/sec. To get heart rate per minute, I multiplied my data by 4, making my uncertainty +/- 4 beats/min. However, what I need to do now is some subtraction, but my uncertainty ends up being much too large...for example:

(72 beats/min +/- 4 beats/min) - (68 beats/min +/- 4 beats/min) = (4 beats/min +/- 8 beats/min)

Have I done this correctly? Is it even possible to have uncertainty larger than the actual value? Thanks!

10

To calculate the heart rate per minute, you multiplied the beats per 15 seconds by 4. This multiplication is correct, so your heart rate values are accurate. However, the way you calculated the uncertainty is incorrect.

When performing subtraction or addition with quantities that have uncertainties, the uncertainties should be added together. In this case, the uncertainties are both +/- 4 beats/min. Therefore, the correct calculation should be:

(72 beats/min +/- 4 beats/min) - (68 beats/min +/- 4 beats/min) = (4 beats/min +/- 8 beats/min)

This means that the difference in heart rate is 4 beats per minute with an uncertainty of +/- 8 beats per minute. Yes, it is possible for the uncertainty to be larger than the actual value. In this case, the uncertainty range extends both above and below the difference in heart rate, indicating that there is significant variability or error in the measurement.

To arrive at the correct uncertainty, you should add the uncertainties together rather than multiply them.