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what is kurtosis method of measurement in data distribution

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Known as the fourth moment, Kurtosis refers to the shape of the distribution of data points about the mean value (known as the 1st moment). Kurtosis is normalized against the variance (2nd moment, also a measure of spread) and set so that the kurtosis of the normal distribution is 0. A more peaked distribution relative to the normal distribution is said to have positive kurtosis, while negative kurtosis is broader than the normal. Accurate measure is highly dependent on the number of samples. 

So, the formulation for excess kurtosis is:

g4 = (m4/m2) = (1/n)*Σ(xi - avg)4 / [(1/n)*Σ(xi - avg)2]2 - 3, where n = number of samples.

In other words, the excess kurtosis is the sum of the difference between the sample value and expected value raised to the fourth power, divided by the square of the sample variance. 


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