Which of the following statements about variance is the most accurate?Multiple ChoiceVariance is the square root of the standard deviation.Variance is the average of the squared deviations from the mean.Variance can be both, positive or negative.Variance is denominated in the same units as the original data.
Question
Which of the following statements about variance is the most accurate?Multiple ChoiceVariance is the square root of the standard deviation.Variance is the average of the squared deviations from the mean.Variance can be both, positive or negative.Variance is denominated in the same units as the original data.
Solution
The most accurate statement about variance is: "Variance is the average of the squared deviations from the mean."
Here's why:
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Variance is not the square root of the standard deviation. In fact, it's the other way around: the standard deviation is the square root of the variance.
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Variance is indeed the average of the squared deviations from the mean. This is the mathematical definition of variance in statistics.
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Variance cannot be both positive and negative. By its mathematical definition (the average of the squared deviations from the mean), variance is always a non-negative number (i.e., zero or positive).
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Variance is not denominated in the same units as the original data. Because it involves squaring the deviations from the mean, variance is actually denominated in the square of the units of the original data.
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