Subject and purpose of work: The work concerns coefficients of asymmetry As and γ the values of which are marked based on coefficients obtained from the sample and serve the description of empirical distributions. These coefficients inform of the strength and direction of asymmetry of distribution. The direction is ruled by the sign of coefficient while the strength-by its absolute value. Since for certain empirical distributions these coefficients have different signs an attemt was made to define the conditions in which such a situation may occur. Materials and methods: Within the conducted research different examples of empirical distributions were considered and simulation methods were applied to establish the condition for occurrence of various signs, including coefficients. This condition is based on the location of arithmetical mean of observation in terms of the range , where D is a dominant of data set and Z is a certain volume also indicated on the basis of the same set of observations. Results: As a result of conducted research it was agreed that both analysed coefficients of asymmetry have the same signs where arithmetical mean is located inside the range and different when it is located outside this range. Conclusions: Within the specific research of the selected feature one should calculate only one of these coefficients.