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What is an absolute value?

What is an absolute value? Here are some definitions.

Noun
  1. (mathematics) For a complex number, the principal square root of the sum of the squares of its real and imaginary parts. Denoted by | |.
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The index of divergence is expressed in the sum of the absolute value of the differences for all industries.
Ignoring minus signs, thereby taking the absolute value, gives a two-part curve.
Figure 4 shows five-year moving averages of the mean absolute value of the ratio of the current account balance to GDP for twelve countries.
The higher the absolute value, more important is the response variable, which enables its sorting in descending order of magnitude.
We then calculated the average absolute value of these discrepancies across all the group members who appraised that participant.
The absolute value of the correlation coefficient represents the strength of the association between the two variables.

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