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I was wondering when a normal distribution can be expected. I know that things like:

  1. heights of people
  2. size of things produced by machines
  3. errors in measurements
  4. blood pressure
  5. marks on a test

    (source: Math is Fun)

follow a normal distribution. But would for example the chosen nicknames of people also fall in that category? And if so or if not, why would that be?

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  • $\begingroup$ Assumption of normality is common among people who don't know any other distribution. $\endgroup$
    – André Nicolas
    Nov 18, 2014 at 15:42
  • $\begingroup$ @AndréNicolas, what other distributions should we take into consideration? $\endgroup$
    – user2609980
    Nov 18, 2014 at 19:33
  • $\begingroup$ The gamma family is useful. There are many others, quite field-dependent. $\endgroup$
    – André Nicolas
    Nov 18, 2014 at 19:47

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Basically, the accumulation of a large number of very small independent contributions will be approximately normal (according to the Central Limit Theorem). For example, take heights of people: if you're talking about a homogeneous population, all adults of the same gender, so that the height differences are the result only of small environmental and genetic differences, the normal distribution might be a good approximation. But if you have males and females, that's a single factor that makes a significant difference (typically around 13 cm), and the deviation from normal distribution will be noticeable. It would be even more noticeable if you had a population consisting of Dutch men and Indonesian women.

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  • $\begingroup$ Thanks. And what about the length (between 0 and 50 characters) of account names a large group of people chooses. Are these a large number of very small independent contributions? Would that result in a normal distribution? $\endgroup$
    – user2609980
    Nov 18, 2014 at 19:31
  • $\begingroup$ I don't know of a reasonable model of that type for choosing account names. $\endgroup$
    – Robert Israel
    Nov 18, 2014 at 20:27

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