Here is the original source of that claim.
Based on the state of medical and surgical practice in 2002, the average American has 3.41 inpatient, 2.56 outpatient, and 3.20 non-OR, for an overall total of 9.17 surgical procedures in an 85-year lifespan.1
The method behind those number was also described. They counted the number of surgical procedures in an 85-year lifespan by summing the rates of surgery for each year between 0 and 84 in Colorado, Florida, and New Jersey based on state databases.1
Citing this work 4 years later, Gawande said, "At the present rate, the average American can expect to undergo seven operations during his or her lifetime."2 Perhaps he did not count the 2.56 outpatient procedures when he claimed "seven operations".
1. Peter H.U. Lee and Atul A. Gawande, The number of surgical procedures in an American lifetime in 3 states, Journal of the American College of Surgeons, Volume 207, Issue 3, Supplement, September 2008, Pages S75
2. Atul Gawande, Two Hundred Years of Surgery, N Engl J Med 2012; 366:1716-1723, May 3, 2012