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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