Skewed Distributions¶
Overview¶
When the data distribution is skewed, the sample mean and median can differ substantially.
Effects of Skewness¶
- Right-skewed: Mean > Median > Mode (e.g., income data, financial returns)
- Left-skewed: Mean < Median < Mode
Estimation Considerations¶
- The sample mean remains unbiased regardless of skewness
- For highly skewed data, the median may be a more representative measure of center
- Confidence intervals for the mean may require larger samples for adequate CLT approximation
Transformations¶
Log or Box-Cox transformations can reduce skewness and improve the performance of mean-based methods.