The number in the middle denotes the character's disposition to you. The higher it is, the more they like you (When you do side-quests for some people, you'll often get their disposition up to the max 100 just by completing the quest for them). Each time you click a segment, the number will either go up or down depending on how large the segment was, and whether it was in a good (smiling character when you hover over it) or bad (unhappy character) part.
So, for example, let's say the largest segment size was equal to 4, the next largest 3, then 2, then 1. And then the four areas either add or subtract the number of the segment you click within them to the total disposition. The 'best' one (with the happiest face), adds two times the number within it, the next best adds one times, then the two bad ones subtract one and two times the numbers. So if you got the largest segment into the best area and clicked it, you'd add 8 to their disposition, and if you got the smallest segment into the worst, you'd only take away 2. Thus, the aim is to get the larger segments in the better two areas, and the smaller in the worse. I don't know how much sense that makes, as said it's kind of a difficult system to explain, despite not being all that complex, but I hope that helps.
As I said before though, if it confuses you, simply click the large segments in the good areas, and it should inevitably go up at least slowly. A character never changes which areas they prefer, so once you figure out which they like and don't, you can rattle through loads of tries really quickly.
EDIT: Also, anyone after Nirnroot (has anyone actually found ten yet? Does he give you the recipe or are you dependent on him stocking you with the potion?), there's 2 or 3 bits of it right against the water's edge on the beack by the Imperial City Docks.
I'm trying to do that mission at the minute, but not having a silver weapon makes it very hard.
