When purchasing a violin and getting the right size it is determined by the size of the individual. The later teens and adults usually get a 4/4, which is full size. It is especially important for young children starting out to be measured and start with the correct size instrument and move up in size as they grow.
The measuring process seems primitive, where the student puts the violin on the left shoulder and chin on the chin rest. Extending the left arm all the way out to the left and cup your left hand. The violin headstock should fit comfortably in the palm of the left hand when you have the right size in hand.
If for example, a young student starts out with a 1/2 size violin and maybe a year later they grow and need the next size violin, this would normally be a 3/4 size. It is a must to buy the needed size so the player will not lose the fingering or positions.
If you go from 1/2 size to a 4/4, the player will lose their natural fingering because of the bigger fingerboard and their fingers are not used to the stretch. The natural progression of the sequenced sizing will allow the player to naturally upgrade as their fingers grow and never feel out of place or lose position.
Student models make sense financially when starting with the smaller instruments and most reputable stores allow the customer to to trade in the older models for the larger sizes as the student grows.