This most likely has to do with your gameplay style more than stats. If possible, upload a video of yourself playing or show us a link to the full match history so we can get a better idea of what a game looks like. If you have trouble closing out games, it probably has to do with your control of minion waves and warding. Get a blue trinket if you have too many items in your inventory.
Place wards so you know when your enemies are coming and when to get out, especially if you are split pushing. That way, you will not die when the enemy team all rush you.
Pushing does not always work if you cannot get into their base. This is the hardest part. It is not just about pushing. You also have to push at the right times. Look at a few pro games and see how they "stack" their minion waves by killing on the caster ones and leaving the melee ones. This will force the enemy to send someone to respond (which you can then kill and repeat) or you can move somewhere else on the map to push a turret.
Option B: Play a champion that pushes insanely hard like Heimerdinger. Very obnoxious and powerful if done right, especially against the unskilled.