Example Uncertainty Propagation

density of a game cube:

Part I:

single measurement of a single cube, accuracy of scale is Δm=0.2g, accuracy of length measurement is Δl=0.1mm

l=20mm, m=200g

Part II:

Now a statistical analysis of a set of three cubes' densities is conducted:

Average of the length:

Standard deviation of the length:

Average of the mass:

Standard deviation of the mass:

Resulting uncertainty of the cube's density: