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I was reading a paper (dont have it with me!) on statistics and found a term that I have never encountered before:

$p_{i}{(x_{i}-\mu )} = p_i(x_i - \sum_i p_ix_i)$

After some research it seems that this term some how to the variance:

$Var(X) =\sum _{i=1}^{n}p_{i}{(x_{i}-\mu )^2}$

Does anyone have a hunch as to what this term referred to in the literature?

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I don't think there is a special name for that term. It's just some mathematical expression,

$$p_i(x_i - \mu),$$

in which the definition of the mean value has been inserted (--where one should better use another letter as $i$ for the summation index),

$$\mu \ = \ \sum_{j} p_j x_j.$$

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