Even my six-cylinder car will only do about 16-17 mpg in my driving (which is mostly city and a lot of short trips). Your typical driving style and your commute (how fast you go, how aggressive you drive, how many times you stop and go) can certainly bring your mileage down to 13mpg with a six-cylinder. If you think you buy a car and you automatically "get" the rated mileage, you are going to find that you're very wrong. Your mileage will depend on how you drive and your particular commute, and remember that there's no limit to how bad your mileage can be, especially if you sit around idling it in the driveway (wasting gas without going anywhere). If you live in LA and you do the 0-90mph-0mph dash all day on your commute, you're going to waste a ton of gas. But if you drive 55mph on rural highways all the time, and learn how to coast to stops, brake less, and drive slower in general, you're going to easily exceed the ratings.
It's hard to make any judgment about whether your fuel economy is "right" unless you log your mileage for a few tanks anyways. This is why I always keep a fuel economy and maintenance log, so I can spot potential issues. For example, before I replaced my thermostat I was seeing 14mpg regularly in the wintertime, and afterwards I immediately saw about a 2mpg improvement.
https://www.fuelly.com/car/bmw/x5/2003/bdc/454415