Standard deviation is defined as which of the following?

Standard deviation is defined as which of the following?

• A. The average distance of scores from the mean.
• B. The variance of the data.
• C. The sum of squared deviations.
• D. The square root of the variance.

Answer: (D)

Standard deviation measures how spread out scores are around the mean. It is defined as the square root of the variance. The variance is the average of the squared deviations from the mean, which gives more weight to larger differences. Taking the square root brings the measure back to the original units of the data, describing a typical distance from the mean. If you were talking about the average distance from the mean without squaring, that would be a different measure (mean absolute deviation). The sum of squared deviations is part of the variance calculation but is not itself an averaged quantity, so it isn’t the standard deviation either. Therefore, the standard deviation is the square root of the variance.

Standard deviation measures how spread out scores are around the mean. It is defined as the square root of the variance. The variance is the average of the squared deviations from the mean, which gives more weight to larger differences. Taking the square root brings the measure back to the original units of the data, describing a typical distance from the mean. If you were talking about the average distance from the mean without squaring, that would be a different measure (mean absolute deviation). The sum of squared deviations is part of the variance calculation but is not itself an averaged quantity, so it isn’t the standard deviation either. Therefore, the standard deviation is the square root of the variance.