I was on vacation and missed posting to this question. Everything Stales said is correct and I've nothing of substance to add - only a small thought.
We have a bunch of raw data - and the data is a pretty good reflection of itself. But looking at a big stack of numbers we often "miss the forest for the trees" and statistics is partly about trying to figure out some way of thinking about the data without thinking about all the components of the data - which we often aren't even capable of doing.
No single number like mean or mode or median is going to give us everything we need to know about the data. There are other things like standard deviation, skew, sample size - all important - but even these don't always cover it. In every case I know or can think of having a large sample size is good. Unfortunately, it's not always practical or possible - and this is where I get a little fuzzy with things and it starts looking like a black art.
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