Which statistic is used to quantify dispersion around the mean and includes the concept of variance and standard deviation?

Which statistic is used to quantify dispersion around the mean and includes the concept of variance and standard deviation?

• A. Range
• B. Variance
• C. Standard Deviation
• D. Interquartile Range

Answer: (C)

Standard deviation quantifies how dispersed values are around the mean and is defined as the square root of the average squared deviations from the mean. This ties directly to variance, since variance is that average of squared deviations, and taking the square root returns the measure to the same units as the data for easy interpretation. In practice, the standard deviation is the go-to measure of spread when the mean is the natural center of the data. Other options describe spread differently: range uses only the extreme values, interquartile range focuses on the middle portion of the data, and variance, while a dispersion measure, does not express spread in the original data units.

Standard deviation quantifies how dispersed values are around the mean and is defined as the square root of the average squared deviations from the mean. This ties directly to variance, since variance is that average of squared deviations, and taking the square root returns the measure to the same units as the data for easy interpretation. In practice, the standard deviation is the go-to measure of spread when the mean is the natural center of the data. Other options describe spread differently: range uses only the extreme values, interquartile range focuses on the middle portion of the data, and variance, while a dispersion measure, does not express spread in the original data units.