In the traditional measurement theory, precision is defined as the dispersion of measured value, and is used as the basis of weights calculation in the adjustment of measurement data with different qualities, which leads to the trouble that trueness is completely ignored in the weight allocation. In this paper, following the concepts of pure probability theory, the measured value (observed value) is regarded as a constant, the error as a random variable, and the variance is interpreted as the dispersion of all possible values of the error. Thus, a rigorous formula for weights calculation and variance propagation is derived, which solves the theoretical problem of determining the weight values in the adjustment of multi-channel observation data with different qualities.