The sum of deviations from the _________ is always zero.*1 pointModeMedianNone of the aboveMean
Question
The sum of deviations from the _________ is always zero.
1 point
- Mode
- Median
- None of the above
- Mean
Solution
The statement you provided refers to a statistical property of the mean. Specifically, the sum of the deviations of a set of data points from the mean is always zero. This occurs because the mean is the balance point of the data set; thus, the positive deviations (values above the mean) and the negative deviations (values below the mean) cancel each other out.
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Concept Explanation: The mean is calculated by summing all data points and dividing by the number of points. When you take each data point and subtract the mean, the total of these deviations sums to zero.
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Example Illustration: For instance, if you have a data set of , the mean is . The deviations are . The sum of these deviations is .
In conclusion, the correct answer to fill in the blank is Mean. This is a fundamental property of the arithmetic mean in statistics.
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