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abarnes98

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Hi,

 

I'm having trouble calculating the uncertainties in an average value.

 

I have obtained several values for VIt (Voltage x Current x Time) and wish to average the values. How do I calculate the uncertainty in the average value of VIt?

 

The issue I'm having is that each value of VIt has a different uncertainty. How do you calculate the uncertainty in the average value if each value     has a different uncertainty?

 

Thanks,

abarnes98

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1. Add all the recorded/calculated VIt values together to get a sum. The uncertainty is the sum of all the absolute uncertainties in each VIt value.

2. Convert this uncertainty to a percentage of the sum.

3. Divide sum by the number of VIt values to get the mean. This division has no error in denominator, only in numerator.  

4. Assign this mean or quotient the same percentage uncertainty from step 2.

5. Change this uncertainty to absolute form, and round to one significant digit.

6. Round the quotient to the same number of decimal places.

EDIT: Step 6 is interpreted as matching the rightmost significant digit of the quotient to that of the uncertainty. Eg. 4327 ± 50  becomes 4330 ± 50

Edited by kw0573
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I'm having trouble calculating the uncertainties in an average value.

I have obtained several values for VIt (Voltage x Current x Time) and wish to average the values. How do I calculate the uncertainty in the average value of VIt?

The issue I'm having is that each value of VIt has a different uncertainty. How do you calculate the uncertainty in the average value if each value has a different uncertainty?

 

According to the Tsokos physics book (2008 version), the IB recommends 2 ways to calculate the uncertainties:

Method 1: Calculate the average (i.e. the mean) of all the absolute uncertainties.

Method 2: Take the range of all the values and divide it by two. In other words, Uncertainty = Range/2. Notice that this method isn’t strictly accurate for a professional lab report because in university, instead of simply taking Range/2, you would have to do standard deviations instead. However, the IB thinks that standard deviations are unnecessary for high school students.

 

So let’s say that you have the results for the Vit values (which are simply the total energies, aren’t they?) like this:

5 ± 1,

6 ± 2, and

7 ± 3, in which the average (or the mean) is: (5+6+7)/3 = 6

 

Then using method 1, the final uncertainty is simply: (1+2+3) / 3 = 2. On the other hand, if you use the method 2, then the uncertainty is: (7-5) / 2 = 1.

Normally you would have to do calculations for both methods on draft papers. Then you compare them and pick the one that gives a higher value for the uncertainty. So in the example above, because method 1 gives a higher uncertainty, you would simply quote the final answer to be: 6 ± 2

 

The reason for all the complications is because the two methods are for two different types of uncertainties. We use method 1 to calculate the propagated error (which is often resulted from the reading errors, emerged when you do the individual measurements). On the other hand, we use method 2 to calculate the random error (which is a measurement of the precision of the experiment). So if the method 1 gives a higher uncertainty, then we say that the experiment is largely influenced by the reading errors. On the other hand, if method 2 gives a higher uncertainty, then the experiment is influenced mostly by the random error.

 

This is the way that I always use to write my lab reports. In practice though, a lot of IB teachers don’t often care about how you actually carry out the calculations for the uncertainty. They just want you to include it in your report, but it doesn’t matter what method you choose to do it. So don’t worry too much!

 

1. Add all the recorded/calculated VIt values together to get a sum. The uncertainty is the sum of all the absolute uncertainties in each VIt value

2. Convert this uncertainty to a percentage of the sum.

3. Divide sum by the number of VIt values to get the mean. This division has no error in denominator, only in numerator. 

4. Assign this mean or quotient the same percentage uncertainty from step 2.

5. Change this uncertainty to absolute form, and round to one significant digit.

 

Hey kw0573, not saying that you're wrong, but isn’t this the same as finding the average of all the absolute uncertainties (which is simply method 1, that I've mentioned above)? In that case, perhaps you might have overcomplicated the problem a little bit in my opinion.

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Hey kw0573, not saying that you're wrong, but isn’t this the same as finding the average of all the absolute uncertainties (which is simply method 1, that I've mentioned above)? In that case, perhaps you might have overcomplicated the problem a little bit in my opinion.

Hi Vioh, this is same as your Method 1. You are correct I did made it more complicated than needs be.

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