Kurtosis
The Kurtosis Calculator helps you measure the "tailedness" of your data distribution - how heavy or light the tails are compared to a normal distribution. This can reveal important patterns in your data, such as whether extreme values occur more frequently than expected. For example, in financial analysis, high kurtosis could indicate a higher risk of extreme market movements.
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Understanding Kurtosis
Definition
Kurtosis is a measure of the "tailedness" of a probability distribution. It quantifies how heavy the tails of a distribution are compared to a normal distribution.
Formula
Sample Kurtosis:
Where:
- is each value in the sample
- is the mean of the sample
- is the number of values
- is the sample standard deviation
Interpretation Guidelines
Visual Examples of Kurtosis
The following examples illustrate how kurtosis affects the shape of a distribution.
Mesokurtic Distribution
Kurtosis ≈ 0
Characteristics: Moderate peak height and tail weight, typical of normal distribution
Similar to normal distribution with balanced tails.
Leptokurtic Distribution
Kurtosis > 0
Characteristics: Taller peak with more concentration of data, thicker tails indicating more extreme values
Higher peak and heavier tails than normal distribution.
Platykurtic Distribution
Kurtosis < 0
Characteristics: Flatter peak with more even spread of data, thinner tails indicating fewer extreme values
Lower peak and lighter tails than normal distribution.
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