Hi OS1--I suppose that those numbers are as good a starting point for an "average" ski as any. Unfortunately, it depends on a lot more, and there is no such thing as an "average ski." I'm 6'1" and about 160 lbs. and the skis I ski on regularly range from 165cm (just above chin height) to 191cm. Occasionally I'll ski shorter than 165cm, and if I were racing downhill or SuperG ("speed events"), I'd go longer than the 191's (which are Giant Slalom race skis).
Ski length depends a lot more on factors other than height. Ski type, conditions and terrain, preferences for speed and turn size...these are the critical factors in finding the "right" ski length.
For a first-time beginner, I would recommend typical beginner skis that are no longer than chin height, as you've suggested. But there are skis much shorter than that that are specially designed for beginners, and that can make the early learning experience very easy and productive and fun. If you are a first-time beginner, or looking for advice for one, I would recommend that you go with what the rental shop at the resort you will ski at has for you. And above all, sign up for lessons. The instructor will help you fine tune your selection as needed, and help you decide when to upgrade.
If you are not a beginner, then you probably know what has worked for you as well as anyone. If you want specific suggestions, or if it's been a while, then by all means take a lesson. At any level of skill, a good lesson will open new doors of enjoyment, and it is the best way to get the personalized advice that you really need.
Good luck with everything. Keep us posted!