What is the measure of variation defined as the sum of deviation of each value from the mean?

• A. Mean
• B. Mean deviation
• C. Median
• D. Mode

Answer: (B)

Measuring variation focuses on how far data points lie from a central value. The measure that uses each value’s distance from the mean and then combines those distances into a single number is mean deviation. Specifically, it’s the average of the absolute deviations from the mean: (1/n) sum |x_i − x̄|. This captures the typical or average spread around the mean, which is what variation aims to quantify. If you simply sum the deviations from the mean without taking absolute values, the positives and negatives cancel out and you get zero, which isn’t useful for dispersion. So mean deviation is the standard way to express how far values tend to lie from the mean. The other options—mean, median, and mode—describe central tendency, not spread, so they don’t measure variation.