Which measure is defined as the sum of squared deviations from the mean?

• A. Range
• B. Standard Deviation
• C. Interquartile Range
• D. Variance

Answer: (D)

Variance uses the idea of deviations from the mean but protects against positive and negative offsets by squaring them, so the dispersion measures don’t cancel out. The variance is defined as the average of those squared deviations from the mean (the sum of squared deviations, often called the sum of squares, divided by the number of observations, or by n-1 for a sample). This focus on squared deviations is what makes variance describe how spread out the data are around the center. Standard deviation is simply the square root of that average, returning to the original units. Range and interquartile range describe spread in other ways (based on extremes or quartiles) and don’t rely on squared deviations, so they aren’t defined this way.