May I ask what is the verb form of statistics or is there any replacement word with the meaning of "the act of doing statistics"?
The term statistics refers to the numbers that are generated by statistical analysis. Perhaps the phrase analyze statistically would meet your needs.
Various specific activities that result in the output of certain statistics have single word verb forms, such as average, correlate, sum, equate, and tally.
Well, Google reports some 300 instances of "statisticked" on the web. And the OED has statisticize, v. To arrange in the form of statistics... to collect or employ statistics....
Perhaps not a perfect match but the word, "figure", as in "figure up the tally" or "Figures never lie, but liars figure".