We analyse the biases of eleven measures for estimating the quality of the multi-valued attributes. The values of information gain, J-measure, gini-index, and relevance tend to linearly increase with the number of values of an attribute. The values of gain-ratio, distance measure, Relief, and the weight of evidence decrease for informative attributes and increase for irrelevant attributes. The bias of the statistic tests based on the chi-square distribution is similar but these functions are not able to discriminate among the attributes of di erent quality. We also introduce a new function based on the MDL principle whose value slightly decreases with the increasing number of attribute's values.