University of Central Florida (UCF) QMB3200 Quantitative Business Tools II Midterm Practice Exam

A data distribution is considered symmetric when it exhibits a balanced shape around a central point, meaning that the left side of the distribution mirrors the right side. One of the fundamental measures of symmetry in statistical analysis is skewness.

Skewness quantifies the degree of asymmetry of a distribution. If the skewness is zero, this indicates that there is no skew and that the distribution is evenly balanced on either side of the mean. When the skewness is zero, one can infer that the tails on both sides of the distribution are of equal length and the peak of the distribution is at the center, reinforcing the idea of symmetry.

Other options suggest a deviation from this balance; for instance, positive skewness indicates that the distribution has a longer right tail, while negative skewness suggests a longer left tail. Similarly, a variance of zero implies that all data points are the same, representing no variability, which does not pertain to the concept of symmetry in distribution forms. Therefore, zero skewness is a adequate indicator of a symmetric distribution.