For answering the "Is this true" part - the easiest way to figure this out is to get the source of the quote. Do you have a source, as in a book or an article, that made that claim? From there, we can at least figure out of the original person who wrote that claim had solid ground for making that statement.
Also, population sizes, average age, child mortality rates, population fertility, and so on can be a dangerous ground to walk upon. I've seen statistics distorted on quite a few occasions. I recollect many conversations that basically go back to, "nobody lived past 40 back then," when the full story is nowhere near that simple.
Okay, now that we found the probable source of the actual number in a primary source (the U.S. Census of 1790 and 1800), some places to find explanation.
I went around a looked, and found that the best place to read more about the population of the United States and the New World is a book called A Population History of North America by Michael R. Haines and Richard H. Steckel. Looking it over, it reminds me of what I've read previously. It appears, the number of children in families was high in the late 18th century, and the rate of children dying was down at the same time. Why did this occur? I would suggest reading the previously mentioned book and I would hope that other historians on this page come in and can offer a more informed and precise explanation.
I just wanted to make sure that the whole thing of life expectancy didn't get misconstrued. Many historians struggled with this issue. One has to take into consideration how much childhood mortality can throw of the life expectancy numbers.
I just want to add that this type of population distribution is not strange for the world of today. In 2000, half of the population of Africa was 18 years old or younger. https://www.un.org/esa/population/publications/worldageing19502050/pdf/81chapteriii.pdf
Here you can see the median age throughout the world currently: https://en.wikipedia.org/wiki/List_of_countries_by_median_age
The median age is getting older worldwide, as women have fewer children and people live longer. But it's not so very long ago that the median age in developing countries was close to the 16 year old range.