The kurtosis of a sample _{1},
x_{2}, ..., x_{n}}, |

K(X) = ((x_{1} - μ)^{4} + (x_{2} - μ)^{4}
+ ... + (x_{n} - μ)^{4})/σ^{4} |

where μ is the mean of the sample X, and σ is the standard deviation. |

If the data X are normally distributed, then K(X) = 3. |

If K(X) > 3, X has large deviations (large tails) and is more peaked. |

If K(X) < 3, X has small tails and is less peaked. |

Return to the Normal Distribution