a common mistake i see lower elo players is make is worrying too much about their statistics. statistics do NOT win you games. they are good sign if you are playing well, but if you are losing and have good stats chances are you're putting too much emphasis on your stats like KDA and CS.
the only stat that really matters if you play carries is "total damage dealt to champions" and kill participation. if your KP is low then thats bad. if your total damage is not top of the charts or close to it, that is really bad usually. sometimes you can't get damage off so take that in mind, but generally speaking as a carry you should be topping the charts if you expect to climb.
CS matters, but i myself cuck my team routinely by choosing to shove out one extra wave rather than start my rotation for a team fight coming up. the key is being able to rotate before a fight breaks. if you are farming and then a fight breaks out and you arent there, that's your bad. you can finish with great cs but if you don't get to team fights from the start you will lose most games as a carry.
focus on objectives. if your team gets kills, ask yourself what can we get? I have cilmbed mostly off my great baron calls and rotations. Not even joking. my mechanics are bad, my cs is relatively bad to my elo, but my team fighting is great, i usually rotate on the important ones and my baron calls on even the smallest of picks (one pick on support for example and then the adc shows bot and we know jungle just backed) have won me so many games.
learn how to prioritize objectives, rotate well, and team fight well. be at every team fight. if you aren't at team fights as a carry that is YOUR fault. very rarely is it because your team fought without you. it seems like it, but ask yourself if you had to back to buy that item or if you had to burn all your mana on that jungle camp before a fight was about to ensue. was dragon spawning, is baron coming up? are we about to siege? all this matters. good back timings is of utmost importance.
