65 As for the reason the average life expectancy of a Roman who reaches the age of 30 being so much higher than the average expectancy overall, that's simply a matter of taking the average of 50 and 80, verses the average of 1,6,20,50,80. Let's illustrate that by calculating the average life expectancy of a Roman at birth, and after age 30. For birth, there's 5 ranges, each of which has the same probability. They are [0,2]: Midpoint = 1. Probability = 0.2. Product = 1*0.2 = 0.2 [2,10]: Midpoint = 6. Probability = 0.2. Product = 6*0.2 = 1.2 [10,30]: Midpoint = 20. Probability = 0.2. Product = 20*0.2 = 4 [30,70]: Midpoint = 50. Probability = 0.2. Product = 50*0.2 = 10 [70,90]: Midpoint = 80. Probability = 0.2. Product = 80*0.2 = 16 Sum = 0.2 + 1.2 + 4 + 10 + 16 = 31.4 But upon reaching 30, there is no longer a mere 0.2 probability for those last 2 slots. The chart looks like [30,70]: Midpoint = 50. Probability = 0.5. Product = 50*0.5 = 25 [70,90]: Midpoint = 80. Probability = 0.5. Product = 80*0.5 = 40 Sum = 65 If you look at each possible range of ages, the actual life expectancy is at birth: 31.4 years after age 2: 39 years after age 10: 50 years after age 30: 65 years after age 70: 80 years