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Can anyone help explain why the following statistics are either Sufficient or not Sufficient?

Mode, Mean, Median, Standard Deviation, Skewness, Kurtosis, Range, IQR

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Perhaps stats.stackexchange.com would be a better venue for this sort of question. –  Jebruho Nov 4 '12 at 22:57
    
Every one of them is sufficient for some family of distributions. Sufficiency is relative to a set of probability distributions. This is explained in this article: jstor.org/stable/2683116 –  Michael Hardy Nov 4 '12 at 23:38
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