mediaanikeskittymä

Mediaanikeskittymä, also known as median absolute deviation (MAD), is a robust measure of statistical dispersion. It quantifies the variability of a dataset by calculating the median of the absolute deviations from the data's median. Unlike the standard deviation, which is sensitive to outliers, the median absolute deviation is less affected by extreme values, making it a more reliable measure of spread in datasets with skewed distributions or significant outliers.

To calculate the median absolute deviation, one first finds the median of the dataset. Then, the absolute difference between each data point and the median is computed. Finally, the median of these absolute differences is determined. This median of the absolute differences is the median absolute deviation. The formula is commonly expressed as MAD = median(|xi - median(x)|).

The median absolute deviation is often used in robust statistical methods, outlier detection, and in situations where data quality might be compromised by extreme values. It provides a more stable estimate of spread compared to variance or standard deviation, especially in exploratory data analysis. Multiplying the MAD by a constant (often approximately 1.4826 for normally distributed data) can provide an estimate of the standard deviation that is comparable to the sample standard deviation. This normalization helps in comparing the dispersion of different datasets.