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!
Calculating uncertainties can be a tricky process, but I'll guide you through it step by step. Let's start with your initial calculation of heart rate per minute by multiplying the data by 4.
Given data: heart rate measured in beats/15 secs
Uncertainty: +/- 1 beat/sec
To convert the heart rate to beats per minute (bpm), you need to multiply the data by 4 since there are 4 sets of 15 seconds in a minute. However, the uncertainty is not directly multiplied by 4 because uncertainties are often treated differently than the actual values in calculations.
So, the heart rate per minute becomes (72 beats/min +/- 4 beats/min).
Now, let's move on to the subtraction step:
(72 beats/min +/- 4 beats/min) - (68 beats/min +/- 4 beats/min)
To subtract these two quantities with their respective uncertainties, you need to combine the uncertainties. When subtracting, uncertainties are added, regardless of their sign. Therefore, the uncertainty of the difference would be the sum of the individual uncertainties:
4 beats/min + 4 beats/min = 8 beats/min
This means that the final result is (4 beats/min +/- 8 beats/min).
To answer your second question, yes, it is possible for the uncertainty to be larger than the actual value. Uncertainty represents the range of possible values within which the true value is likely to lie, based on the measurement precision and the nature of the equipment used. In this case, the uncertainty of the difference between the two heart rates of 72 bpm and 68 bpm is larger because the uncertainties are added together.
Do note that uncertainties can accumulate and become larger as you perform calculations involving multiple steps, as seen in this subtraction. It's always important to consider and properly propagate uncertainties to ensure that the final result reflects the overall accuracy of the measurements and calculations involved.