Why does literature list the strong coupling at the scale of the Z-boson's mass? In the 2004 edition of the book "QCD as a Theory of Hadrons" by S. Narison, the author provides a value for the strong coupling at a scale of the mass of the Z boson, 
$$ \alpha_s (M_Z) = 0.1181 \pm 0.0027 \tag{11.68}$$
This is a footnote explaining the choice of the scale: 

[$\tau$ decays give] so far the most precise measurement of $\alpha_s$ at $M_Z$ as a modest accuracy at the $\tau$-mass becomes a precise value at the $Z$-mass because the errors decrease faster than the running of $\alpha_s$. Also, here, compared with some other determinations, we have relatively the best theoretical control including the perturbative corrections to order $\alpha_s^4$, the non-perturbative condensates and the resummation of the asymptotic series. (sic)

Apart from a possible typo in the first sentence, I do not understand this reasoning. 

Also the PDG states on page 4 of their QCD review (PDF link) that 

it has become standard practice to quote the value of $\alpha_s$ at a given scale (typically the mass of the $Z$ boson, $M_Z$) [...]

 A: These are the measurements of the strong coupling constant .


Running of the Strong Force Strength
The plot  shows the running, or evolution, of the strength of the strong interaction.  This is characterized by the evolution of the strong coupling constant aS, plotted here versus  energy scale in GeV. This plot is taken from the Particle Data Group.

Look at the measurement error at the tau,just below two GeV, and the meaurement error at the Z just below 100 GeV.
The errors for measured quantities include the statistical errors, the systematic errors of the actual measurements and the estimated errors due to the mathematical formulae used to get at the measured value.
In the case of $a_s$ the contribution to the error by the theoretical model is much better known at the Z, than at the tau energy, thus one uses the value measured at the Z. After the Z the errors are larger. 
The plot justifies the the errors decrease faster than the running of $a_s$ only for the beginning of the curve, for the measured erros,  so the statement is not really supported by the measurement error behavior observed in the plot. The green width must be the theoretical errors.
