Q:

accurate measurements with less accurate tools

Is there a good way to systematically increase the accuracy and precision of a measuring tool using only mathematical means?  For example, average 10 measurements from the same tool can create a better measurement. Or using two independent tools and average them.  I don't know if measuring theory or statistical quality control or other subject can help.

A:

If you know that the errors in your measurements are truly random and have a normal distribution then you can improve the resolution of a measurement by taking several measurements and averaging them. This technique is called oversampling and is common in digital data acquisition systems where the hardware resolution may be low.
You mentioned accuracy, which is the difference between a measured value and the true value. This technique will not improve accuracy. If a measuring device is inaccurate it will still be inaccurate if you average a bunch of measurements. If you want accuracy you must calibrate your measuring tools against another tool that is known to have better accuracy...and so on back to NIST (in the U.S.)
The word precision usually implies repeatability. I don't think you can get rid of something like long-term drift or temperature affects just by averaging multiple samples.

