We are a family of 5, & I honestly couldn't tell you how many loads of laundry we do per week.
We have a stackable washer & dryer, & DH built shelves to go beside the washer & dryer. On each shelf is a basket - one for darks, one for lights, one for socks & underwear, & one for towels & sheets.
Everyone is supposed to bring their dirty clothes down to the laundry room. That doesn't happen very often.
However, if all has worked according to our "system," when a basket is full, I do a load of laundry.
Most of the time what happens is, when I get ready to do a load of laundry, I'll say, "I'm getting ready to wash socks & underwear. Do y'all have any socks and underwear in your rooms that need to be washed?" And, then, from out of nowhere there'll be a stampede, & the one load of dirty socks & underwear turns into 2-3 loads.
Typically, the basket w/ the dark clothes gets full the fastest. If I don't stay on top of it, it can quickly turn into an overstuffed & overflowing basket w/ extra piles on the floor.
The towels & sheets basket is never full. When I'm ready to wash towels, I have to go around collecting dirty towels & asking for dirty towels out of bedrooms.
Sometimes, I'm not in a laundry "mood," & I'll let all the baskets get full & then have a laundry marathon day & might do 4-6 loads in one day.
In the summer, there's more laundry due to beach towels being washed nearly every day.
But, no, I can't say that I ever do 15 loads/week on a normal basis.