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### Topic: Uncertainty - how to calculate?  (Read 53043 times)

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#### tou

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• Mole Snacks: +0/-0 ##### Uncertainty - how to calculate?
« on: November 16, 2008, 05:14:28 AM »
Hi I am looking for the method to calculate the total uncertainty of measurements.

When we do labs, we always have a independent and dependent variable. So, for example, when we investigate "how temperature affects reaction xy" we use different temperatures (e.g. 5) and measure the reaction of xy by using a gas syringe (for example). We also do 3 trials for every temperature. I know the uncertainty of the thermometer (1) and the gas syringe (0.1).

What I am looking for is, if you take the average gas volume for every temperature, how do you calculate the uncertainty? I've read that you use the standard deviation, but I am not sure if that's the right method.

Also, I want some kind of total uncertainty for all averages. In my raw data table, my uncertainty for all data would simply be "0.1" for the gas syringe. That would apply to all my measurements of gas. But, when I calculate the average gas volume, and the according uncertainties, the uncertainties could differ for each average. I tried out the standard deviation, and for the first average the uncertainty was 0.2 and for the second 0.1 (I just made that up for this case). Now I don't want 5 individiual tables for my 5 averages (because I have 5 temperatures). I want one table with all my 5 temperatures and the according gas volume averages. Also I want the total uncertainty for all my averages together. How do I calculate this total uncertainty?

I hope I am not confusing...

Thanks!!

#### jansenwrasse

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• Mole Snacks: +0/-2 ##### Re: Uncertainty - how to calculate?
« Reply #1 on: November 16, 2008, 09:09:01 AM »
you should know what temperature you are expecting to get then from there:

take 3 measurements X, Y, and Z respectively X+Y+Z
------  x 100%
Mean

Average diviation/ mean x 100%

#### tou

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• Mole Snacks: +0/-0 ##### Re: Uncertainty - how to calculate?
« Reply #2 on: November 16, 2008, 09:48:18 AM »
you should know what temperature you are expecting to get then from there:

take 3 measurements X, Y, and Z respectively X+Y+Z
------  x 100%
Mean

Average diviation/ mean x 100%

What do you mean with average diviation?

If I have the table:

--------------- gas volume (0.1)
Temperature (1) - trial 1 - trial 2 - trial 3
25 ----------- result 1 - result 2 - result 3 (or X, Y, Z) -> average
30 ----------- result 4 - result 5 - result 6 -> average
35 ----------- result 7 - result 8 - result 9 -> average

I want a table, which only shows the averages and the combined uncertainty.
By calculating the percentage uncertainty, I calculate the uncertainty for when I take the average?

(result 1 + result 2 + result 3) / 3 = average 1 (unc. ?)

Now I am not quite sure what you mean with (X+Y+Z)/mean, because when you do that, you get the number of measurements taken and then multiply it by 100?

The table I would like to have:

------------------- gas volume (uncertainty ?)
Temperature (1) --------------------------
25 ----------------- average 1
30 ----------------- average 2
35 ----------------- average 3

#### enahs

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• Gender:  ##### Re: Uncertainty - how to calculate?
« Reply #3 on: November 16, 2008, 10:10:59 AM »