A series of numbers can be represented by the mean (average), the mode (most frequent) and the median (middle number).

The mean is the most commonly used everyday statistic, but sometimes the median provides more insight. For example, the median house price is a better gauge than the average price as the nature of housing stock units across the whole economy tends to remain the same and therefore the middle number is a better representation of the state of housing.

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From 'IntroSTAT', by Les Underhill and Dave Bradfield:

The normal distribution is the most important distribution in statistics. Part of the reason for this result called the 'central limit theorem', which states that if a random variable X is the sum of a large number of random increments, then X has the normal distribution.

The daily turnover of a large store is the sum of the purchases of all the individual customers. The height of a 50-year old oak tree can be thought of as the sum of each year's growth - which itself is a variable affected by sunshine, temperature, rainfall, etc. So one expects the heights of 50-year old oak trees to obey a normal distribution. Similarly, an examination mark is the sum of the scores in a large number of questions. Thus, by the central limit theorem, one expects daily turnover, the heights of trees and examination marks (approximately, at least) to be normally distributed.

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