A small village of ice miners has popped up in the Northern Territory. They are a mix of southern workers who integrated with the native tribes. The group subsists on the meat of a single humpback whale per year. They worship the giant fish creatures as gods, and preform ritualistic sacrifice to justify the killing of a whale. How many people can survive off of a single whale? Some money is made from selling ice, but most of it goes into improving the tribe's houses and buying new supplies for the diggers.
My calculations are very rough. The average weight of a humpback whale is about 25-30 tons, according to Wikipedia.
I didn't manage to find any sources for this, but I've seen the estimates of whale bone being about 20% of its weight, leaving us with around 22 tons of muscles, internal organs and blubber. And if they do not eat anything but whale, they are going to need the icky stuff, maybe some of it even raw, to be supplied with vitamins and microelements.
Now the hardest part is estimating the calorie value of a whale. I didn't manage to find exact figures for a humpback. (Here is the data for other whale kinds: Whale Meat in Nutrition)
As you can see, it ranges from 110s for lean meat to 400-500 for blubber and some internal organs. I would try averaging that to 190-200 kcal per 100 of 'average' whale product. That would give us about a kilo of edible whale meat and other icky stuff per person to keep them alive and active enough to hunt the next whale.
Dividing 22 tonnes per 365 days we get about 60 kilos of whale per day. So, with all the allowances I've made at the every step of the calculation, it seems that an average whale would be able to feed 60 (possibly less, if I overestimated the mass of edible portions or average caloric value) people per year, if they are ready to eat it whole.
UPD: if you are basing them of indigenous Arctic people, most of their societies are busy looking for food all year round. They, most likely, won't rely on one risky hunt per year - they will gather berries and roots, even edible lichens, hunt for birds, seals and whatever land animals there are (white bears, different kinds of deer), fish almost constantly. If they live that way, you can adjust the estimate upwards for at least 2x.