What are skewness and kurtosis?

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Skewness and kurtosis are statistical measures that describe the shape of a data distribution.

Skewness – Measures asymmetry of the distribution.

  • Skewness = 0: Symmetrical distribution (e.g., normal distribution).

  • Positive skew (right-skewed): Tail extends more to the right; most data is on the left.
    Example: Income distribution—many earn less, few earn much more.

  • Negative skew (left-skewed): Tail extends more to the left; most data is on the right.
    Example: Test scores where most students score high.

Kurtosis – Measures the "tailedness" or peakedness of the distribution.

  • Kurtosis ≈ 3 (normal distribution): Called mesokurtic.

  • High kurtosis (>3): Leptokurtic – more extreme outliers, heavy tails, sharper peak.

  • Low kurtosis (<3): Platykurtic – fewer outliers, light tails, flatter peak.

Why They Matter:

  • Skewness tells you if the mean is pulled left or right of the median.

  • Kurtosis tells you how likely you are to see extreme values (outliers).

Example:

Imagine exam scores:

  • Skewness > 0: Most students failed, but a few did very well.

  • Kurtosis > 3: Most scores are near the average, but a few are very high or low (outliers).

Summary:

  • Skewness = direction of asymmetry

  • Kurtosis = heaviness of tails (outliers)

These measures help analysts understand distribution shape and decide if data meets assumptions for statistical tests.

Read More

What is hypothesis testing?

Explain Bayes’ Theorem with an example.

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