Just looking for the population of Narvik it's currently 15k & was around 5k before WW2. So taking your 1:8 ratio would be looking at 40k German troops & I just wonder where they'd put them all as you don't want to live under canvas during a Norwegian winter.
Two comments: first, the 1:8 ratio was the other way around. The Norwegian population was about 2.5 million; the German garrison was about 300,000 for most of the war. So per your analysis, the German garrison would have been more like 630...a weak battalion.
But second, the 1:8 ratio I mentioned was observational, just comparing national totals...not, AFAIK, some sort of local-garrison-numbers assignment metric.
We know from historical commentary that the Germans assigned the Norway garrison primarily to the locales where they thought the Allies might want to attack...that is, primarily Narvik because of the overriding importance to the Germany military economy of iron ore from the northern Swedish mines during the frozen-Gulf-of-Bothnia months, plus the other ports to the north even though unlike Narvik they mostly were not ice-free during the winter months, plus all the airfields along the Norwegian coast.
Much of the ~ 2.5 million WWII Norwegian population lived in the southern urban areas, but the Germans didn't consider those areas to be particularly at risk of Allied military action so didn't heavily defend them, other than the harbors and airfields. Most of the defenses and corresponding garrisons were disproportionately to the north.