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  • I am measuring the temperature of a metal plate using 4 thermal sensors.
  • The sensor used is specified to have an accuracy of ±0.1°C.

If I have for example those readings:

enter image description here

The average of all sensors is: 20.45°C.

However how should I report the accuracy?

My intuition is that:

  • The lowest reading (20.3°C) could be as low as 20.2°C because of the sensor reported accuracy.
  • The highest reading (20.6°C) could be as high as 20.7°C.
  • That covers an 0.5°C range.

So I would conclude that the accuracy of my sensors average is ±0.25°C

Is this correct?

Francois
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  • Is there reason to believe that the temperature will be absolutely uniform across the plate, or could there be persistent temperature variations between different points? – Brian Borchers Mar 29 '24 at 21:06
  • No the temperature across the plate is most likely not perfectly uniform. – Francois Mar 29 '24 at 21:09
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    If every reading is too high by $.1$ then the average will be too high by $.1$, and similarly on the low side. Thus your average has the same accuracy as the individual sensors. Not sure why you are just looking at min to max....you aren't reporting the temperature of the sample, just the average, right? – lulu Mar 29 '24 at 21:11
  • The accuracy of the sensor is a property of the sensor, it has nothing to do with the average temperature of the plate. – Paul Mar 29 '24 at 21:16
  • Yes I'm only reporting the average. – Francois Mar 29 '24 at 21:16
  • Note that, unless the errors are strongly correlated, you actually expect the average to be more accurate than the individual readings, as it's likely that some of the errors will cancel. Of course, it's possible that the errors are too correlated for that. – lulu Mar 29 '24 at 21:26
  • If these were four independent measures of the same quantity, then you would report the standard error of the mean. But that doesn’t apply here. – Brian Borchers Mar 30 '24 at 02:00
  • Unfortunately, without making some sort of assumption about the spatial correlation of the temperature of the plate at different points, you can't put an uncertainty on the average temperature over the plate. This is a problem with uncertainty in spatial variability of the temperature, which goes far beyond any measurement error. This has been called the "point to pixel problem." – Brian Borchers Mar 30 '24 at 02:50

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