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No, it is not possible.

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โˆ™ 2015-07-23 10:49:18
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Q: Is it ever possible for the iqr to be larger than the range?
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By definition, a quarter of the observations are at most as large as the lower quartile. Therefore it is possible to have an observation, X, which is smaller than the lower quartile, L. That is X <= L Again, by definition, a quarter of the observations are at least as large as the lower quartile. Therefore it is possible to have an observation, Y, which is larger than the upper quartile, U. That is U <= Y So X <= L <= U <= Y Therefore U - L <= Y - X That is, the IQR must be less than or equal to the range.

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