This is from a 15-26 and looks close enough to fit an improved family, but its' a wild guess and you have to take measure. Sooner or later a parted up machine will turn up on ebay or some where else. You probably should only have one spool pin, maybe two on some versions, there rest of them are oil points. One of them should be on the bed for the bobbin winder.
Here's a large picture of an improved family, the bobbin winder shows the fitting screw and shape. Improved Family went through some changes too, so there's a lot of details to get right.