Nollakeskiarvolla

Nollakeskiarvolla, a Finnish term meaning with zero mean, is used in statistics, data analysis, and signal processing to describe a random variable, a stochastic process, or a data sequence whose expected value or arithmetic average is zero. In probabilistic terms, a random variable X is zero-mean if the expectation E[X] equals zero; a time series {X_t} is zero-mean if E[X_t] = 0 for all t. For deterministic data, a dataset has zero mean when the arithmetic average of its values is zero.

The concept is central to data centering, where the sample mean is subtracted from observations to produce a zero-mean dataset. Centering is a common preprocessing step before applying methods such as principal component analysis, linear regression, or Fourier analysis, because it removes the DC component and can improve numerical stability.

In signal processing, a zero-mean signal lacks a constant offset. A zero-mean white-noise process has an average value of zero and typically constant variance, with no predictable direct current component. However, zero mean does not imply the absence of structure; the signal may still exhibit variance, autocorrelation, or other patterns.

Applications of the zero-mean concept extend from model diagnostics (where residuals are assumed to be zero-mean) to normalization procedures in machine learning and time-series analysis. The term emphasizes the idea that positive and negative deviations balance around zero, rather than implying a lack of information or variability.

See also: centering, mean subtraction, DC component, zero-mean processes.