How do skewness and kurtosis affect interpretation of descriptive statistics?

• A. High skewness indicates asymmetry; kurtosis reflects tail heaviness; both affect mean/SD and normality assumptions.
• B. Skewness affects only the mode; kurtosis only affects the median
• C. They have no impact on descriptive statistics
• D. They only affect data visualization

Answer: (A)

Distribution shape matters for describing data. Skewness and kurtosis capture aspects of shape that go beyond just the center and spread.

Skewness tells us about asymmetry. If a distribution is not symmetric, the mean tends to be pulled toward the longer tail, while the median is more robust. This means the mean and standard deviation may not accurately summarize the data when skew is present, and normal-model assumptions are often violated.

Kurtosis describes tail heaviness and peakedness. Fat tails mean more extreme values and outliers, which can inflate the standard deviation and affect the accuracy of normal-based inferences. Low kurtosis indicates fewer extreme values.

Together, skewness and kurtosis inform whether standard descriptive summaries and normal-theory procedures are appropriate, or whether transformations or nonparametric approaches are better.

High skewness indicates asymmetry; kurtosis reflects tail heaviness; both affect mean/SD and normality assumptions.