Examples[edit]

Basic example[edit]

Given two school classes — one with 20 students, one with 30 students — and test grades in each class as follows:

Statistical properties[edit]

Expectancy[edit]

The weighted sample mean, ${\bar {x}}$ , is itself a random variable. Its expected value and standard deviation are related to the expected values and standard deviations of the observations, as follows. For simplicity, we assume normalized weights (weights summing to one).

If the observations have expected values

Bevington, Philip R (1969). Data Reduction and Error Analysis for the Physical Sciences. New York, N.Y.: McGraw-Hill. 300283069.

OCLC

Strutz, T. (2010). Data Fitting and Uncertainty (A practical introduction to weighted least squares and beyond). Vieweg+Teubner. 978-3-8348-1022-9.

ISBN

David Terr. . MathWorld.