Paint

This is what the floor looks like right now. I went to Home depot and got all the grey/gray paint chips they had.

So far I really like Sterling (780E-3), it seems to me to be the most pure, without blue or purple or yellow undertones. It is a bit darker than I was thinking of for the living room, but more or less what I had imagined in the bedroom. I know they can mix paint, can they just mix it with a pure white to make it lighter, or does that change the tone? The next color up on the card I don't like as much, it looks more purple to me.

There are various pictures of the color online but they all look way more blue to me than the card does.