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If $Q_1, Q_2, Q_3$ are the quartiles of a set of data and $$Q_3 - Q_2 = Q_2 - Q_1$$does that indicate a normal distribution?

naslundx
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Mathperson
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2 Answers2

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It is an indication that you have a symmetrical distribution. This could be the uniform distribution, the triangle distribution or the normal distribution as you said. To check symmetry you also need further indications such as that the mean is almost equal to the median.

Jimmy R.
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  • Could you give an example of a uniform distribution that is not a normal distribution? – Mathperson Mar 20 '14 at 13:23
  • @Mathperson Do not confuse "uniform" with "symmetrical". Look here for the uniform and look here or here for symmetrical triangle distribution. – Jimmy R. Mar 20 '14 at 13:28
  • @Mathperson Look also here for the bi-modal distribution, which is another example of symmetrical distribution, which satisfies your condition, but which is not normal, and (not even approximately normal, as for example the triangular distribution, which "looks like" normal) – Jimmy R. Mar 20 '14 at 13:36
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No, it doesn't. For instance: the uniform distribution also has this property.

Nick Peterson
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