I believe the average height for a man is at 5'9". The female being 5'4" or 6", I cannot recall. And to the question of the average height of a man in 1800. You can fairly assume it is about the same or, if somewhat shorter, only marginally so. And also, height would also depend on a number of things such as country, relative wealth of country, economic station, etc. In other words, on the average, an undernourished waif from the gutters of London will likely turn out to be shorter than a farm hand.

Patricia