The sum of observations' deviations equals zero when measured relative to_________________?
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Answer: A. Mean
Explanation
The arithmetic mean serves as the mathematical balance point of a dataset where positive and negative distances equalize. Subtracting the mean from each observation generates deviations whose negative and positive values perfectly cancel out. Consequently, the algebraic sum of all deviations measured relative to the arithmetic mean always equals zero. The arithmetic mean is the most common measure of central tendency used in statistical data analysis. Mathematical derivation of least squares properties relies heavily on this fundamental zero-sum property of deviations. Extremes in a dataset can heavily influence the arithmetic mean because every single value is included.
Option B measures the most frequent value, and deviations from it do not necessarily sum to zero. Option C represents the middle position value, which minimizes absolute deviations rather than algebraic deviation sums. Option D measures overall data dispersion and does not possess a balancing point property for raw deviations.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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