Wrms
WRMS stands for Weighted Root Mean Square, a statistical measure that generalizes the ordinary root mean square by incorporating weights for each data value. It is used to quantify the overall magnitude of a set of numbers when some observations are more important or reliable than others. In practice, WRMS is common in experimental analysis, sensor data interpretation, and calibration tasks where measurement uncertainties vary across samples.
For a set of values x1, x2, ..., xn with corresponding nonnegative weights w1, w2, ..., wn, the
WRMS = sqrt( (sum_i w_i x_i^2) / sum_i w_i ).
If the weights reflect measurement uncertainties, a common choice is w_i = 1/σ_i^2, where σ_i is the
WRMS reduces to the ordinary RMS when all weights are equal. It is related to, but distinct
Applications include error analysis (weighted root mean square error), sensor fusion, calibration of instruments, and any