I'm currently working my way through a lab report, and I'm running into a couple problems that are still slightly above my level / I'm having a terrible brain fart. I was wondering if someone might be able to clarify a couple questions that I have? Any insight or advice that you guys could provide would be greatly appreciated!

So the first issue:
I'm measuring a given object and I'm supposed to include its uncertainty.
For the first object, I took three measurements:
5.20 +/- 0.03 , 5.15 +/- 0.02 , 5.15 +/- 0.02

This then brings me to the first question that I'm having issues with: What is the average of those three values? Ignoring the errors, the value would be 5.17. How do I include the uncertainties, though? Do I also average the uncertainties?

My second question is also derived (no pun intended) from this original question: What is the first derivative of this? Do I graph those three values, find a best fit line, and then use that graph equation to plug it into the derivative equation?

I'm pretty lost.

If you need any further information to help me out, please let me know.
Thank you!

If you know for a fact that your measurements are correct, then the only possible value is 5.17

I know I'm not helping for the general case with uncertainties, but...

The measurements above were merely done with a ruler. Errors will exist, sadly.

Here's the information relevant to the first part of this lab. I'm not asking you guys to do this for me, I just want to simply understand how to calculate the asked values based upon the data that I collected.

Instructions:
http://i.imgur.com/MOpoLLB.jpg

Tables (I need help with the averaging of the uncertainties and how to do the derivatives):



Analysis (this is where it explains what is expected after you've collected the data):
http://i.imgur.com/bOV6PP6.jpg

What does it mean by"left,center, right "?

It's merely denoting as to where the measurement was taken on the object. The measurements were taken on the left side of the block, the center of the block, and the right side of the block in order to avoid any potential variables (such as the wood warping or not being completely smooth).

o
to answer your earlier question, it never asked for the uncertainty of your avg, at least not in your sense

it wants the standard deviation



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for the multiplication parts use

remember to bring the "z" over to the right side

x,y,etc are your measured values
delta x,y,etc are your uncertainties
z= your answer , delta z= uncertainty of your answer




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and, i'd like to point out your uncertainties of .02,etc for the ruler and such
usually, your uncertainty is going to be one half of your most precise marking
so, taking a ruler usually measures to millimeters, then uncertainty is .0005 m, or .05 cm

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from http://www.rit.edu/~w-uphysi/uncertainties/Uncertaintiespart2.html

This post was edited by saber_x3 on Aug 28 2013 11:47am

That second part answered my question about uncertainties perfectly, thank you! With that said, I won't be needing that anymore due to the fact that I took your advice and adjusted all of my uncertainties to 0.05 cm. Thus, my averaged value is a hell of a lot easier to calculate, as the uncertainty will remain 0.05 throughout.

For the derivative part, would you be willing to take three of my data values and quickly show me how to calculate that value? I'm currently in Calculus, however, we haven't even started to cover these types of topics. I mainly just need to know where to plug things in.

If you do have the time and are willing to quickly show me how to take the standard derivative, here's my first three values and their average:
7.70 +/- 0.05 cm
7.70 +/- 0.05 cm
7.70 +/- 0.05 cm
Average: 7.70 +/- 0.05 cm

Thank you very much, though, for the assistance thus far!

x_i, X sub i is your measured value(s) ,7.7
u= your calculated mean,7.7

the big E is just summation
you do it for how many data points you have

so [(7.7-7.7)^2 + (7.7-7.7)^2 + (7.7-7.7)^2 ] =0

so,basically your std dev is 0, since you're summing up zeros to get 0 then multiplying by (1/(n-1)) , taking square root at the end
n= number of data points
--
this can be easily confirmed by your 3 measured values; they were all the same
there was no deviation from the mean, no dispersion

Ah damn, I gave you the easy one, then
Thank you for taking the time to help me, man.

Since n is the number of data points, the value for n, this case, would be 4 , right? Or would you exclude the average, and only count the three measurements as data points?
For example, on the next set I have the points:
5.20 +/- 0.05
5.15 +/- 0.05
5.15 +/- 0.05
Avg: 5.17 +/- 0.05

Plugging these values in:
= sqr[((1)/(4-1)((5.20-5.17)+(5.15-5.17)(5.15-5.17))^2]
= 0.006

Sorry for the formatting issues, i'm doing this on my phone.

No, n is the number of measured data points, the average is a calculated value
n=3
sqrt[[(5.2-5.17)^2 + (5.15 -5.17)^2 + (5.15 -5.17)^2] *(1/(3-1))]