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The mean alone does not provide any information about the higher order moments of the distribution of the data set. Most important amongst these is that it does not give information about the variance - or the spread of the distribution. The data set could be distributed in a narrow band about the mean or spread more evenly over a wider range. It does not tell you anything about the skewness, that is whether there are many values smaller than the mean balanced by a few large values (or the other way around). Moments of the fourth or higher order are difficult to comprehend and, in most cases, ignored.

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14y ago
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Q: What does the mean not tell you about a data set?
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