# Measurement uncertainty

1. Nov 11, 2014

### gnurf

In an attempt to determine how the temperature varies over a distance of 100m, I have taken five temperature measurements for every 10 meters, for a total of 55 measurements. I have then, for each dataset of N=5, calculated the mean value, standard deviation and standard error. Finally, I've plotted the mean value with error bars in what I believe is the most accurate and informative way to represent this data (mean temperature on the y-axis, and distance on the x-axis).

So far so good I think, but how do I include the accuracy of the, say, 3 1/2 digit measurement equipment if it was specified as accurate to within +/- 5% and +/-3 digits?

Last edited: Nov 11, 2014
2. Nov 11, 2014

### dlgoff

3. Nov 11, 2014

### gnurf

Thanks, but I didn't find what I was looking for at that url.

What I described above is basically a four step process (measure-->calculate mean-->calculate standard deviation-->calculate standard error) and I'm wondering at what stage it makes the most sense to take the 5% accuracy of the sensor into account. E.g., can I slap it onto the end of said four step process and simply increase the standard error by 5% (I'm guessing not, but I'm asking in order to clarify the problem).

4. Nov 11, 2014

### dlgoff

Okay. You want Propagation of Uncertainty.

This looks good for that: http://www.rit.edu/cos/uphysics/uncertainties/Uncertaintiespart2.html#propagation [Broken]

from http://www.rit.edu/cos/uphysics/uncertainties/Uncertaintiespart2.html [Broken]

Last edited by a moderator: May 7, 2017