Perhaps the fault is with the way the phrase is structured.
The average person in the Middle Ages probably had a life expectancy into the late 30s or early 40s.
That means that, with regard to the law of averages, half the people died before their 30s and half the people died after (such that averaging out, the age was, say 38. To get there, all things considered, half the population died from ‘birth’ to age 38, and half the population died at 39, 40, 41, etc.)
Again, when my father was born the average life expectancy for a male (at birth) was 47 years. That meant that roughly half the men born that year would die at or before age 47, and half later. He lived into his 60s; his mother, who had been born in the 1870s and whose life expectancy at birth was about age 50, made it to age 100.
And that does make sense. A young man would die say before age 38 if he died in a war, in a famine, from overwork, in a plague of some type, or from some now ‘curable’ disease; mumps, measles, a pox, a respiratory ailment, appendicitis, etc.
But here’s the thing. The older one got to a point, the more likely he or she barring accidents could expect to live ‘longer’ than the average. We see that today; nonagenarians, barring accident or illness, already having passed the ‘life expectancy’ of the mid to later 80s, are more likely to live to the age of 100 than a person who is currently, say, 50, again all things considered.
But of course, plenty of nonagenarians die. Plenty of 50 year olds live to be nonagenarians, too.