Ace Descriptive Stats & Probability 2026 – Unlock the Fun in Numbers!

The standard deviation measures how spread out the data are around the mean. It is defined as the square root of the variance—the variance being the average of the squared deviations from the mean. Taking the square root brings the measure back to the same units as the data, making it easier to interpret the typical distance from the mean. The sum of squared deviations is part of the variance calculation, but the standard deviation is not simply that sum. The mean describes central location, not spread. Squaring the variance would describe a different quantity with a different interpretation. So the standard deviation is best described as the square root of the variance.