Even seemingly obvious assumptions can be surprising when confirmed by actual facts and figures.

That was how I felt when I came across a handful of datasets from the real estate website Zillow. While they predictably offer a wealth of information about home sales, one of the more interesting things I discovered was data showing the median rental price of homes listed on the site. I've charted the data below.

A young couple stands in front of their home.

Image source: Getty Images.

As you can see, the going rental rate is far from static. While it varies, however, there's an easily discernible pattern. Between April and September the advertised rental price goes up. And between October and March it heads back down.

While this makes perfect sense -- as I said above, the trend is consistent with common sense – what makes it interesting is the magnitude of the difference and the related realization of how much you could potentially save by waiting until the winter to sign a lease and move.

By signing a lease in January 2011 as opposed to April of the same year, for instance, the average renter would have saved 20%. That's the equivalent of getting slightly more than two free months of rent. And while the difference isn't quite as robust in the following years, it's nevertheless present.

Now, there are some obvious trade-offs. For one thing, depending on where you live, moving may not be quite as appealing in the winter as it is in the spring or summer -- unless you live in Texas or Arizona, that is. For another, these trends correspond closely to the educational calendar: When school is out, college students move. And finally, there are presumably fewer places to choose from in the colder months, as that time of year corresponds to the middle of others' tenancies.

What's the lesson here? If you already assumed this cyclical pattern to be the case, then there's little to gain other than a little pride at being confirmed right. Alternatively, if you weren't aware of this and are in a position to exploit it, then doing so could end up saving you a good chunk of change.