16. VarianceThe variance, denoted with the symbol S2, is the mean of the squared deviation scores. Because the variance is responsive to the value of each score in a distribution, the variance uncovers differences in variability that less sophisticated measures of variability (e.g., range) do not.
The numerator of this expression, the sum of the squared deviations from the mean, has its own abbreviation; it is known as the sum of squares, or SS.
The variance finds its greatest use in more advanced statistical procedures, particularly in statistical inference.
The calculated value of the variance is expressed in squared units of measurement. Not only is a “squared word" difficult to understand in its own right, but the squaring is problematic on more technical grounds as well: If the scores of one distribution deviate twice as far from the mean as those of another, the variance of the first distribution will actually be four times as large as that of the second. Because of this, the variance is little used for interpretive purposes.
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