How can weather statistics, such as the day's average temperature and degree
days be "really" accurate while the temperatures through the day often don't
rise and fall in a smooth fashion.

For example, on a recent day here in Cleveland, Ohio, (9/29) the high was
73 degrees, which occurred somewhere right after midnight, and the low was
47 degrees, probably late evening. The hourly summary showed 72 degrees at
the 00:51 and 01:51 morning readings, and the 73 degree high must have been
at an odd moment. A front came in, and within two hours, temperatures were
in the 50's, and stayed there, dropping slightly throughout the day,
bottoming out at 47 degrees for the day's low, but showed 49 degrees for the
23:51 reading.

So the days average temperature was stated as 60 degrees with 5 heating
degree days. However if you took the temperature each hour and added it up,
and divided it by 24, the real average would more likely be in the low to
mid 50's, with 10 or 12 degree days.

This kind of thing happens frequently here, especially in the winter.
Sometimes we get nights where temperatures go up into the 50's or 60's for a
few hours, seemingly just ahead of a cold front that will have us back into
subfreezing temperatures by sunrise and the rest of the day.

Also, during the summer, for example, even if you had a day with a high of
85 and a low of 65, wouldn't the average generally run higher that 75 due to
the longer day, with more than half the hours usually above 75 degrees, and
the opposite true in winter, bringing the real average a little under? With
the present scenario, I can't see how degree days would be a very accurate
reflection of how much energy would be used to heat or cool a home.