Which dispersion measure equals the square root of the average squared deviations from the mean?

Which dispersion measure equals the square root of the average squared deviations from the mean?

• A. Standard deviation
• B. Variance
• C. Range
• D. Variation ratio

Answer: (A)

The main idea is that dispersion around the mean is captured by the standard deviation: it takes the squared deviations from the mean, averages them, and then takes the square root, giving a measure of spread in the same units as the data. This square-root step is what distinguishes standard deviation from the variance, which is just the average of the squared deviations without taking the root. The range, by contrast, uses only the difference between the maximum and minimum values and says nothing about how all the other values are spread in between. The variation ratio is a statistic used with categorical data to describe how dispersed the data are relative to the mode, not to quantify numerical dispersion around the mean.

The main idea is that dispersion around the mean is captured by the standard deviation: it takes the squared deviations from the mean, averages them, and then takes the square root, giving a measure of spread in the same units as the data. This square-root step is what distinguishes standard deviation from the variance, which is just the average of the squared deviations without taking the root. The range, by contrast, uses only the difference between the maximum and minimum values and says nothing about how all the other values are spread in between. The variation ratio is a statistic used with categorical data to describe how dispersed the data are relative to the mode, not to quantify numerical dispersion around the mean.