Can I Accurately Measure Temperature with 3 1/2 Digit Equipment?

[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?

 

[dlgoff]

Where to start? Here maybe?

http://www.ni.com/white-paper/4439/en/

 

[gnurf]

Where to start? Here maybe?

http://www.ni.com/white-paper/4439/en/

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).

 

[dlgoff]

Okay. You want Propagation of Uncertainty.

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

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

 

[alphy]

I would first like to commend you on your thorough approach to measuring temperature over a distance of 100m. Your method of taking multiple measurements and calculating the mean value, standard deviation, and standard error is a sound and reliable way to analyze the data.

In regards to your question about the accuracy of the 3 1/2 digit measurement equipment, it is important to note that this type of equipment is not typically used for precise temperature measurements. 3 1/2 digits refers to the number of digits displayed on the equipment, which in this case would be 3 and a half digits. This means that the equipment can display a maximum value of 1999, with each digit representing a value from 0 to 9. This level of precision may be suitable for certain types of measurements, but for temperature measurements, it may not be sufficient.

Furthermore, the stated accuracy of +/- 5% and +/-3 digits means that the actual temperature could vary by 5% of the measured value, plus or minus 3 digits. This can result in a significant margin of error for your measurements, especially when considering the small temperature differences you may be trying to detect over a distance of 100m.

To address the accuracy of your equipment, I would recommend using a more precise and calibrated thermometer, such as a digital thermometer with a higher number of digits (e.g. 4 or 5 digits) and a smaller margin of error. This will provide more accurate and reliable temperature measurements for your study.

In terms of including the accuracy of your equipment in your data representation, you could mention it in the methodology section of your study or include a note or disclaimer in your graph. However, it is important to note that the accuracy of your equipment may have a significant impact on the overall accuracy and reliability of your results.

In summary, while your approach to measuring temperature over a distance of 100m is commendable, it is important to consider the limitations of your equipment and to use more precise and calibrated instruments for accurate temperature measurements.