# Lab, uncertainty

I have a lab and I'm having a hard time calculating or even understanding how to calculate the uncertainty.

It wants me to calculate the uncertainty of temperature.

Here is my data:
time (mins) Temp (°C)
2 23.2
4 26
6 29
8 31.5
10 33.5
12 35.5
14 37.6
16 39.7
18 41.8
20 43.9

Don't I need some given value and divide the average by it? And I also don't understand how I'm suppose to calculate the uncertainty when the readings of the temperature was taken at different times...
Help! Am I going crazy or did I do my lab wrong?

cepheid
Staff Emeritus
Gold Member
Can you give the EXACT wording of the question in your lab assignment that asks about uncertainty?

EACH temperature value has an uncertainty associated with it due to the fact that your measuring instrument is not infinitely precise. In fact, your measuring instrument seems to be precise only to a tenth of a degree. Therefore, just as an example, you have no way of knowing whether the temperature at 8 minutes was 31.50 or 31.53 or ... whatever. The thermometer doesn't measure that finely.

In principle it could have been anywhere in the range of 31.45 to 31.54, (If it was an analog thermometer with tick marks, you'll assume the human being looking at it will try to figure out whether it was less than halfway between two ticks or more than halfway between them. If it was a digital thermometer, you assume it follows some reasonable quantization rules that correspond to our rounding rules.) This is one reason why a good rule of thumb is that the experimental error could be considered to be HALF the precision of the measuring instrument (0.05 degrees in this case). As a result, we'd express the temperature as:

$$31.5^{\circ} \textrm{C} \pm 0.05^{\circ} \textrm{C}$$

Anyway, can you see what the point of all of this estimation of experimental uncertainty is? Can you see that the precision of the thermometer limits how *certain* we can be about the actual temperature, and that the degree of certainty is expressed by the number of significant figures, and clarified by the experimental error that we tacked on?

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