Streuungsschätzung

Streuungsschätzung refers to the process of estimating the variability or dispersion of a dataset. In statistics, understanding how spread out data points are is crucial for drawing meaningful conclusions. Common measures of dispersion include the variance and the standard deviation. When dealing with a sample of data, we use these sample statistics to estimate the population variance and standard deviation. The sample variance, typically denoted as s², is calculated by summing the squared differences between each data point and the sample mean, then dividing by the sample size minus one (n-1). This division by n-1, known as Bessel's correction, provides an unbiased estimator of the population variance. The sample standard deviation, s, is simply the square root of the sample variance. The choice of estimator depends on the specific context and assumptions about the underlying data distribution. For instance, if the data is known to be normally distributed, these estimates are particularly reliable. In cases with outliers or skewed distributions, alternative measures of spread like the interquartile range might be preferred. Accurate streuungsschätzung is fundamental for hypothesis testing, confidence interval construction, and model fitting.