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What effect does squaring the deviations have on values far from the mean?
AIt places great weight on the far values
BIt removes the far values from the count
CIt caps the far values at the mean value
DIt turns the far values into negative ones
Answer & Solution
Correct answer: A. It places great weight on the far values
1. Squaring a deviation of 10 gives 100, while squaring a deviation of 100 gives 10,000.
2. The penalty therefore grows much faster than the distance itself.
3. Values far from the mean carry great weight in the variance, so outliers can make the standard deviation very large.
4. Squaring makes every deviation positive, so it cannot turn far values negative.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.7 Measures of the Spread of the Data_
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