Fractional Error and Differentiation

[Soaring Crane]

The following was gathered in an experiment.



r(m)----- N1------N2-----N3----N4-------N5---N_avg---delta N
0.001---131------139---175---140-----158----148.6----15.882
0.002----90-------96---102-----87------85----92------6.228
0.003----52-------53----73-----65------55----59.6----8.139
0.004----53-------53----55-----39------54----50.8----5.946
0.005----26-------45----34 -----24------36-----33-----7.537

delta N = stand. dev. of row

The formula that describes the relationship among these variables is:

Strength of source = (4.3*10^-10)*[N(r^2)/d^2] curies, where d was found to be 0.02 m and delta r = 5*10^-5 m.

Find the error (delta s) of strength of the source.

I took the derivative of the formula:

delta s = (4.3*10^-10)/(d^2)*[(deltaN/N) + (2deltar/r)]

However, I don't know where to go from here to find /\strength.

How do I used this formula with all the individual /\N's, N_avg values, and r values?

I did do a graph of r vs. N^-1/2 and found the slope of the regression line,

where strength = (4.3*10^-10)(slope)^2/(d^2) and the line's slope is equal to Nr^2. (The value d is a constant here.)

Please I really need help. Thank you for any replies.

 

[haruspex]

You have committed (ahem) a ‘standard error'. You want the uncertainty in the mean of a set of values forN, not the uncertainty in each reading. This is known as the standard error of the mean. https://en.wikipedia.org/wiki/Standard_error.
I haven’t checked how you calculated the "delta N" values. I assume it was by dividing by n-1 (=4), not by n, before taking the square root. If so, you now need to divide each delta N by √n, i,e. √5.
From there, you can apply $\frac{\Delta s}s=\frac{\Delta N}N+2\frac{\Delta r}r$