According to this
table, our family of 5 (1 7 year old boy, one 16 year old boy, two adults in their 40s and a woman in her 70s) would spend about $180 to $310 a week depending on thrifty to liberal (and of course, this doesn't take into account location - these are averages). I live in a very expensive part of the US. Food is expensive here.
We spend at the grocery store per week about $300. BUT that includes all meals, AND a couple times a month we have some event I need to bring food for for a LOT of people. It also includes all snacks AND all cleaning supplies, toiletries, kitchen paper products, etc. (paper towels, napkins, coffee filters, sandwich bags, etc.) We never go out to eat, so there is no additional cost thrown in there either.
When you take out the "other" stuff. We probably spend about $250-$275 a week on pure groceries.
And I think we do pretty well. That is organic dairy and eggs, fresh produce, high quality foods. The only processed food I buy is protein bars - if you call that processed.