Standard deviation measures how dispersed the values are around the __________________.

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

Answer: (A)

Standard deviation measures how much the data values spread out around the central value. It uses the mean as the reference point because deviations from the mean are squared and averaged to give a single number that reflects typical distance from that center. In other words, it quantifies dispersion around the average value, not around a median, mode, or the extremes alone. The mean acts as the balancing point that minimizes the squared deviations, which is why standard deviation specifically describes spread around it. For example, with values 2, 4, 6, the mean is 4, and the standard deviation shows how far 2 and 6 lie from 4 on average, capturing the typical deviation from the center. The median describes a middle position, the range only captures the total spread between extremes, and the mode indicates the most frequent value—none of these directly quantify dispersion around the central value the way standard deviation does.