dispersionskoefficienten

The dispersion coefficient, also known as the coefficient of dispersion or relative mean absolute deviation, is a statistical measure used to quantify the variability of a dataset relative to its mean. It is particularly useful when comparing the dispersion of datasets with different means.

The dispersion coefficient is calculated by dividing the mean absolute deviation (MAD) by the mean of the dataset. The mean absolute deviation is the average of the absolute differences between each data point and the mean of the dataset. Mathematically, if X is a random variable with mean μ and absolute deviation |x - μ|, then the MAD is E[|X - μ|]. The dispersion coefficient (V) is then expressed as V = MAD / μ.

A higher dispersion coefficient indicates greater relative variability in the data, meaning the data points are, on average, further from the mean in proportion to the mean itself. Conversely, a lower dispersion coefficient suggests less relative variability.

This measure is dimensionless, making it suitable for comparing the dispersion of variables measured in different units or on different scales. For instance, it can be used to compare the price volatility of two different stocks, even if their average prices are vastly different.

While the dispersion coefficient is a useful tool, it has limitations. It is sensitive to outliers, and it is undefined if the mean of the dataset is zero. In such cases, other measures of dispersion, like the coefficient of variation (which uses the standard deviation instead of the MAD), might be more appropriate.