The inverse problem of finding the characteristics of latent sources of atmospheric aerosol pollutants based on monitoring data is considered. When solving such problems, the measured values of the pollutant concentration in the general case differ from their mathematical expectations. The data dispersion is due to the statistical nature of the process of atmospheric pollutant propagation and the presence of measurement errors. We propose a method for taking account of dispersion of the measured concentration values. We also determine the probability of falling the unknown source of impurity in a given region and lying its power in a given range of values.