The history of many fields of science can be divided into a small number of time intervals that often begin with some important discovery.
But I have never seen something similar in timeline of statistics.
Obviously, there are some important dates that can be considered as starting points of a new period (Pascal+Fermat, Bayes, Pearson, Tukey,..).
Can we at least very roughly divide history of statistics into small number of periods?
Note that the only similar question to this is related to only famous statisticians, not to periods in history.
These recent papers by Stigler, where he argues (convincingly I believe) for the types of periods you seem to have in mind.
Stigler, Stephen M. 2010. Darwin, Galton and the statistical
enlightenment. Journal of the Royal Statistical Society: Series A
Stigler, Stephen M. 2012. Studies in the history of probability and
statistics, L: Karl Pearson and the Rule of Three. Biometrika 99(1):