Which of the following measures would be useful for commenting upon the degree…

Concept

A statistical distribution has separate descriptive features: location, spread, balance between its two tails, and tail weight.

Moment-based summaries distinguish these features: the third standardized central moment tracks tail imbalance, whereas the fourth standardized central moment is associated with tail weight.

Application

To assess asymmetry, use the measure based on the third standardized central moment. Its sign indicates whether the longer tail lies to the right or left, and its magnitude indicates how pronounced the imbalance is. This measure is skewness.

Contrast

• Central tendency summarizes location through measures such as the mean, median, and mode.

• Dispersion summarizes spread through measures such as the range, variance, and standard deviation.

• Kurtosis is based on the fourth standardized central moment and is used to discuss tail weight or outlier propensity.

Result

Skewness is the measure used to describe the degree of asymmetry in a statistical distribution.