On average, how long will a broken finger take to be back to normal?

Finger fracture. Can heal quickly but there are many structures in the hand that combine to give function. Adjacent joints may be slightly arthritiic and be inflamed, tendons and ligaments can be stiff or tight, skin can stay swollen, joints can be inflamed.Muscles can be weak from injury or disuse.Pain in some degree can be from even a slight subtle change in mechanics.Handtherapy can help at times. Times vary.
Fracture type? Takes at least 4 months for edema and reactive swelling to resolve and 8 to 10 months to reach endpoint with regard to range of motion. Type of fracture and treatment modality will greatly effect time frame.