Kurtosis
- Quantifies how concentrated data are around the mean versus in the tails.
- Distinguishes distributions with sharper peaks from those that are flatter compared to a normal distribution.
- Helps characterize a dataset’s shape to support understanding of population characteristics and to make inferences.
Definition
Section titled “Definition”Kurtosis is a statistical measure that describes the shape of a distribution. It is defined as the degree of peakedness or flatness of a distribution relative to the normal distribution.
There are two types of kurtosis: excess kurtosis and normal kurtosis. Excess kurtosis is a measure of the amount of peakedness or flatness of a distribution relative to the normal distribution. Normal kurtosis is a measure of the peakedness or flatness of a distribution relative to the normal distribution.
Explanation
Section titled “Explanation”Kurtosis indicates how data points are distributed around the mean and how many observations lie in the tails of the distribution. A higher kurtosis corresponds to a distribution where observations are more tightly concentrated near the mean with relatively fewer observations in the tails; a lower (or flatter) kurtosis corresponds to a distribution where observations are more evenly spread around the mean with relatively more observations in the tails. Both excess kurtosis and normal kurtosis compare this peakedness or flatness to that of the normal distribution.
Examples
Section titled “Examples”Excess kurtosis example
Section titled “Excess kurtosis example”A distribution with a high degree of peakedness or sharpness: data points are concentrated around the mean, with a small number of data points in the tails. Example: the distribution of test scores for a class where most students scored near the average, but a few students scored very high or very low.
Normal kurtosis example
Section titled “Normal kurtosis example”A distribution with a moderate degree of peakedness or flatness: data points are spread out evenly around the mean, with a relatively equal number of data points in the tails. Example: the distribution of heights for a population of adults, where most people are of average height, but some people are taller or shorter than average.
Use cases
Section titled “Use cases”Kurtosis can provide insights into the concentration of data points around the mean and the spread of data points in the tails of the distribution, which can be useful for understanding the underlying characteristics of a population or data set and for making predictions or inferences about the distribution.
Related terms
Section titled “Related terms”- Excess kurtosis
- Normal kurtosis
- Normal distribution