# Measurement uncertainty: Standard uncertainty of the mean

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1. Oct 26, 2014

### garyd

1. The problem statement, all variables and given/known data
Hi,

I am doing some basic X-ray analysis and trying to quantify the measurement uncertainty associated with my determined value for the K-α line of copper. I have obtained the x-ray spectrum from a copper target using a detector and multichannel analyzer (No. of pulses/pulse height as a function of energy in keV). I have identified and isolated the K-α peak. I have fitted a Gaussian/Normal distribution curve to the data, computed the mean value in keV and have computed the sample standard deviation. I now need to compute the standard uncertainty of the mean and I’m unsure of the correct method. As far as I know the standard uncertainty of the mean (u) is given by [1] below where N is the number of measurement readings taken in order to determine the mean value and sigma n-1 is the computed sample standard deviation.

2. Relevant equations

U=σn-1/N [1]

3. The attempt at a solution
The multi-channel analyzer effectively sorts and counts incident voltages of different magnitudes. I have an array of x-axis data in keV. e.g. x=[2 3 4 5 4 3 2] I am wondering is N the length of the array (=7) or the sum of the array (23)

2. Oct 27, 2014

### haruspex

Shouldn't that be $\sigma_{n-1}/\sqrt n$?

3. Oct 27, 2014

### garyd

Yes it should be $\sigma_{n-1}/\sqrt N$
But what value is N

4. Oct 27, 2014

### haruspex

N is the number of values (which is why I wrote n; it's the same n as in σn−1).

5. Oct 27, 2014

### garyd

Sorry i was referring to my lecture notes, n makes a lot more sense, thanks