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The expected value of a random variable; or a location measure for a sample.

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Zero-sum property of the difference between the data and the mean

I am new in statistical studies and on this site and I came across the "zero-sum property" in my book regarding the mean. … The only information it gives with the formula is the sum of the difference between each value of a variable $Y$, noted $Y_i$, and the mean value of $Y$, noted as $\bar Y$, is equal to zero. …
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