Skewness, Kurtosis & Identifying Outliers with Z-Score

Reading Time: 8 Mins | Level: Intermediate

1. Distribution Shape: Skewness & Kurtosis

• Skewness: Measures asymmetry of the distribution:
• Symmetric ($Skew \approx 0$): $Mean = Median = Mode$.
• Right / Positive Skew ($Skew > 0$): Long tail on the right. $Mean > Median$. (Common in wealth, revenue, response times).
• Left / Negative Skew ($Skew < 0$): Long tail on the left. $Mean < Median$. (Common in human lifespan, test scores).
• Kurtosis: Measures "tailedness" and likelihood of extreme events:
• Mesokurtic ($Kurt \approx 3$ / Excess $\approx 0$): Standard normal distribution.
• Leptokurtic ($Excess > 0$): Fat tails, high risk of black-swan outliers.

2. Detecting Outliers using Z-Scores

The Z-Score measures how many standard deviations an observation lies from the mean: $$Z = \frac{x - \mu}{\sigma}$$

Observations with $|Z| > 3.0$ are statistically classified as extreme outliers: