Interval data, a special case of symbolic data, is becoming more and more frequent in different fields of applications including the field of Data Mining. Measuring the dissimilarity or similarity between two intervals is an important task in Data Mining. In this paper an analysis of ten desirable properties that should be fulfilled by the measures for interval data for making it suitable for applications like clustering and classification has been done. Also, it has been verified whether these properties are satisfied by three existing measures- L1-norm, L2-norm, L∞-norm and also a new dissimilarity measure for interval data has also been proposed. The performance of all the existing distance measures are compared with the proposed measure by applying well known K-Means algorithm on 6 interval datasets. It is seen that proposed measure gives better clustering accuracy then the existing measures on most of the datasets.