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What are averages?

What are averages? Here are some definitions.

Noun
  1. plural of average
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Over the next month we will be hearing rather a lot, yet again, about those 99 years, the law of averages, and luck.
Perhaps, but it'll more likely be the law of averages, a destiny thing, a twist of fate.
In the early 18th century, the English mathematician Roger Cotes computed weighted averages of measurements made by different astronomers.
Given the small slice of the population these privileged backgrounds represent, we have here a spectacular breakdown in the law of averages.
He took over a bunch of players that was accustomed to losing, but expected, on the law of averages, to win one day.
Figure 4 shows five-year moving averages of the mean absolute value of the ratio of the current account balance to GDP for twelve countries.

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