Which statistic is the average of squared deviations from the mean?

• A. The average deviation from the mean
• B. The standard deviation
• C. The sum of squared deviations from the mean
• D. The average of squared deviations from the mean

Answer: (D)

The main idea is that averaging the squared distances of data points from the mean defines a measure of spread called the variance. Squaring the deviations ensures every distance contributes positively and larger deviations count more, so the result reflects how spread out the data are. When you take the square root of that average, you get the standard deviation, which is on the same units as the data. The sum of squared deviations is just the total without averaging, so it’s not the measure of spread. The average deviation from the mean would imply averaging deviations without squaring (or using absolute values), which gives a different statistic. Therefore, the description that matches is the average of squared deviations from the mean—the variance.