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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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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.
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 ratio of this force to the mean absolute value of the force exerted by each surrounding zone is the unbalanced force ratio.
The number above each segment gives the rank of the absolute value of the monotonic increase or decrease.

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