Couldn't tell you about how it's calculated, I assume some kind of survey of skeletons from that period as you can fairly easily tell the broad age range of skeletons from their development.

As for the average age, it's a common fallacy amongst the general public that the average death age amongst Classical and Medieval people means that their lives were in Hobbes' famous words ' nasty, brutish and short'. You're quite right to think that this isn't really true, plenty of people in these periods lived well past their 40s even those living in poverty. It is as you say the large number of infant fatalities that dragged the average down and this is simply a function of maths and averages. Large numbers of child fatalities will drag down the average age substantially because they are dying in the 0-3 age range thus skewing the figures away from people dying at 50, 55 and even 60. If you look at famous figures of the period, although they lived in luxury and are somewhat unrepresentative for your average person, they weren't dying off in their early 40s due to disease and poor medical knowledge. Henry VIII was famously unhealthy and lived to 55, Charlemagne lived to 71, Pompey the Great 58 and Caesar 55 and both of them didn't suffer natural deaths, Augustus was 75, Samuel Pepys to go a little further down the social ladder died at 70, Geoffrey Chaucer son of wine makers lived to 56, Bede (English historian and monk) lived to 62 and so on and so on.

These days our medical ability has advanced to such a stage that in the developed world the idea for a mother dying in childbirth or children dying in their infancy is considered a tragedy and is thankfully rare. In the past it was all too common and a large number of women would have lost at least one child during their lives. It's also a reason for having relatively larger families as you can't rely upon children surviving their infancy, you can still see this in parts of the developing world such as India and Africa, where children die in far greater numbers than the Western World (although there are also socio-cultural reasons for large families as well).

Another totally unrelated misconception around health in these periods is that these people must have had hideous dental hygiene. That's not really true either, with the lack of sugar in their diets their teeth were often better than our modern equivalents. Sure they probably weren't cosmetically attractive with the lack of braces, wisdom tooth removal etc. but this idea we have of ignorant smelly peasants with no teeth in their mouth dying at 40 is all wrong.

I was trying to find my source material for this, but it comes from a class I took on Roman Demographics at Berkeley. At Rome, infant mortality (death at ages 0-5)was about 50%. This dragged down the life expectancy dramatically. As for population models, a lot of it is used off of analogues. In this case, it was compared to sub-saharan africa. There was a giant book of population models, but for the life of me I can't remember the name.

Anyways, if you lived to be 5, you stood a pretty good chance of living a relatively long time. Roman men married at around 30. It was somewhat uncommon for men to marry and have their fathers around still. Grandfathers were particularly uncommon. They know all this because under Roman laws, you're under the legal authority of the paterfamilias until he dies (and ultimately, most married men were the paterfamilias when they got married). So yes, many people lived until well into their fifties and even sixties. It had a lot to do with malarial resistance in the Roman context.

One of the earliest sources that really has good data on this, while still being in an age when medicine was fairly primitive, is Halley's life table.

You can compare it to modern life tables if you like. I think the basic takeaway is that mortality was higher in all periods of life, but that there wasn't some dramatic early death cutoff. There has never been a period when, for example, 20 year olds were unlikely to make it to 25 (barring, say, Mongol invasions, smallpox epidemics, and the like), but it used to be much more common for a 20 year old to die before 25 than it is today. (In Halley's sample, for example, 95% of 20 year olds make it to 25. In the US today, I think 99.5% of 20 year olds make it to 25.)

So, it was really neither "everyone makes it to 35 and falls over dead" nor "half of infants died, then everyone who survived infancy lived to 70." There was somewhat higher mortality throughout life, with infancy perhaps being the most dangerous.

Question - surely, average life expectancy would also be squewed by maternal childbed death? The age of man might be three score and ten, but I don't expect the age of woman was.

In addition to a lot of people dying as children (and life expectancy is just a mean age of death, as best as we can tell from our sources), a lot of people died early from other things (accidents, various diseases etc). That didn't meant that people of 70 or 80 years were unheard of, just that there was a higher chance you would die of something else first. This is different than people being 'old' at 40.