Based on techniques developed in the previous papers of this series , we investigate the impact of galaxy-cluster mergers on the order statistics of the largest Einstein radii .
We show that the inclusion of mergers significantly shifts the extreme value distribution of the largest Einstein radius to higher values , typically increasing the expected value by { \sim } 10 \% .
A comparison with current data reveals that the largest observed Einstein radius agrees excellently well with the theoretical predictions of the \Lambda CDM model at redshifts z > 0.5 .
At redshifts z < 0.5 , our results are somewhat more controversial .
Although cluster mergers also increase the expected values of the order statistics of the n largest Einstein radii by { \sim } 10 \% , the theoretically expected values are notably lower ( { \sim } 3 \sigma deviation for n = 12 ) than the largest Einstein radii of a selected sample of SDSS clusters in the redshift range 0.1 \leq z \leq 0.55 .
The uncertainties of the observed Einstein radii are still large , however , and thus the measurements need to be carefully revised in future works .
Therefore , given the premature state of current observational data , overall , there is still no reliable statistical evidence for observed Einstein radii to exceed the theoretical expectations of the standard cosmological model .