What are skewness and kurtosis?
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Skewness and kurtosis are statistical measures used to describe the shape of a data distribution.
Skewness measures the asymmetry of a distribution around its mean. A perfectly symmetrical distribution, like the normal distribution, has a skewness of zero. Positive skewness indicates that the tail on the right side (higher values) is longer or fatter than the left side, meaning most data points are concentrated on the lower end. Negative skewness means the left tail (lower values) is longer, with most data clustered toward higher values. Skewness helps identify biases in the data and deviations from symmetry.
Kurtosis measures the tailedness or the concentration of data around the mean. It indicates whether the distribution has heavy tails or light tails compared to a normal distribution. A normal distribution has a kurtosis of 3 (mesokurtic). High kurtosis (>3, leptokurtic) suggests more data is in the tails and peaks, implying extreme values are more likely. Low kurtosis (<3, platykurtic) indicates a flatter distribution with fewer extreme values.
Together, skewness and kurtosis provide insights beyond mean and variance, helping analysts understand asymmetry, outliers, and the overall shape of the data distribution. They are essential in fields like finance, quality control, and machine learning to assess risk, anomalies, and model assumptions.
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