Streuungsmaßzahlen

Streuungsmaßzahlen, also known as measures of dispersion or spread, are statistical values that describe the variability or scatter of a dataset. They quantify how much individual data points differ from each other and from the central tendency of the data. Understanding dispersion is crucial because it provides insights into the reliability and representativeness of summary statistics like the mean. A dataset with low dispersion indicates that data points are clustered closely around the mean, suggesting less variability. Conversely, high dispersion implies that data points are spread out over a wider range, indicating greater variability.

Commonly used Streuungsmaßzahlen include the range, which is the difference between the maximum and minimum values in a dataset. While simple to calculate, the range is sensitive to outliers. The variance measures the average of the squared differences from the mean. Squaring the differences ensures that all values are positive and gives more weight to larger deviations. The standard deviation, the square root of the variance, is often preferred because it is expressed in the same units as the original data, making it more interpretable. Another important measure is the interquartile range (IQR), which is the difference between the third quartile (75th percentile) and the first quartile (25th percentile). The IQR is less affected by extreme values than the range and is particularly useful for skewed distributions. These measures collectively help in comparing the spread of different datasets and assessing the risk or consistency associated with them.