# Lab Report Calculating Average Uncertainties - various methods, which is correct?

## Recommended Posts

Hey Guys,

For AGES, our class has been having disputes about how the average uncertainty is calculated in physics.

Here are 2 options that we are confused between

So if we want to know the Avg uncertainty and values are 44.3 ± 0.2 , 44.7 ± 0.2, 44.9 ± 0.2 and 44.1± 0.2

1) Average uncertainty = (Max value - Min value)/Total number of values

Avg uncertainty = (44.9-44.1)/4

We got this from an IB Physics uncertainties book... I can't remember how old it was but i think maybe around 2007 or more recent.

But this seems outrageous! You honestly can't just do that can you?!?!

2) We think it should be the way we do it in chem and maths and everywhere else!

Avg uncert = Total sum of uncertainties/Total number of values taken

Avg uncert = (4*0.2)/4

Avg uncert = 0.2 !

This is sooo much more logical.

And at the same time they say that you need to take the greater uncert value, which is just 2 in this case.

The problem is that method 1 gives you the same uncertainty (±0.2) in this example, but in various other problems that we have had in class it gives a greater uncertainty than ± 0.2 and it is illogical to use a greater value as the uncertainty.

How do you guys calculate Average Uncertainties?

##### Share on other sites

Actually, the physics textbook is right, under the condition that you separate the uncertainties into uncertainties due to random error and uncertainties due to instrumental error.

1.) This is actually the correct method for calculating random error. You take the highest and lowest value of your measurements and divide by TWO.

Uncertainty due to random error = (44.9-44.1)/2

Uncertainty due to random error = 0.4

2.) This is the method for calculating instrumental error uncertainties. It is the summation of all absolute uncertainties divided by the number of trials.

Average Uncertainty due to instrumental error = 0.2

Then, you would have to decide whether you will use uncertainties based on instrumental error or random error. In this case, you would use random error uncertainties because they are higher. It's pretty similar to doing graphical analysis in your lab reports where you take the highest and lowest gradients for your uncertainties.

The source for all this is the IB Physics study guide, by Tim Kirk (I believe?)

Edited by by.andrew
• 2

##### Share on other sites

Thank you soo much! Dividing by 2 makes so much more sense and thank you for clarifying that there are two different situations where the different averages are used.

And I never thought about it as being the same as the graphical analysis!

##### Share on other sites

Just use standard deviation when dealing with averages. I find that it makes more sense.

##### Share on other sites

The only time you should use standard deviation is when your raw data generates a graph like a motion sensor. Then, if you were to find average velocity, you would take the standard deviation or RMSE of the velocity points. For analysis, never use standard deviation as it you will lose marks in dcp.

And im happy that I could help !

##### Share on other sites

The only time you should use standard deviation is when your raw data generates a graph like a motion sensor. Then, if you were to find average velocity, you would take the standard deviation or RMSE of the velocity points. For analysis, never use standard deviation as it you will lose marks in dcp.

And im happy that I could help !

Hello Andrew,

Our physics teacher told us that we should use the standart deviation to find the uncertainty of a value which is the average of -let's say- five values. But you are saying that we will lose marks by doing so. Are you sure? Is my physics teacher wrong? I am currently writing my lab reports and I want to be sure on this issue. Can you share us a formal IB document regarding this issue?

Eflatun

##### Share on other sites

The only time you should use standard deviation is when your raw data generates a graph like a motion sensor. Then, if you were to find average velocity, you would take the standard deviation or RMSE of the velocity points. For analysis, never use standard deviation as it you will lose marks in dcp.

And im happy that I could help !

Hello Andrew,

Our physics teacher told us that we should use the standart deviation to find the uncertainty of a value which is the average of -let's say- five values. But you are saying that we will lose marks by doing so. Are you sure? Is my physics teacher wrong? I am currently writing my lab reports and I want to be sure on this issue. Can you share us a formal IB document regarding this issue?

Eflatun

Hey there,

This was a while ago, but I think what I tried to say is that standard deviation is not a good way of calculating error if your experimental approach is susceptible to (potentially significant) random error or involves analogue measurements. Usually in high school labs, this is usually the case, so I think comparing random error and the instrumental uncertainty is quite effective. I didn't say you would lose marks for using standard deviation for averaging values, but I think you'll lose marks if you use stan. dev. in graphical analysis (see below).

Your teacher may be right in certain circumstances where random error is not very prominent (at least in the macroscopic scale). Since your physics teacher will be the one marking your IAs, I suggest you ask him about it, and ultimately, follow his rules.

And for graphical analysis, you should never get your uncertainties using standard dev. This should be in your textbook/study guide. You draw your error bars and get the steepest gradient/shallowest gradient and compare slope or y-intercept this way.

Edited by by.andrew

##### Share on other sites

Hey guys,

does anybody know how to calculate the uncertatinty of an average of averages?

In physics we are calculated the average verlocity of the horizontal component of a trajectory using the velocity points, and we used the standard error of the mean formula to calculate the uncertainty of the average. We did that for several experiments

Now we want to calculate the average of those average velocities. How do we calculate the uncertainty of that average???

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account. ×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.