Traditional data processing in science and engineering starts with computing the basic statistical characteristics such as the population mean E and population variance V. In computing these characteristics, it is usually assumed that the corresponding data values x1,...,xn are known exactly. In many practical situations, we only know intervals [xi-,xi+] that contain the actual (unknown) values of xi or, more generally, a fuzzy number that describes xi. In this case, different possible values of xi lead, in general, to different values of E and V. In such situations, we are interested in producing the intervals of possible values of E and V -- or fuzzy numbers describing E and V. There exist algorithms for producing such interval and fuzzy estimates. However, these algorithms are more complex than the typical data processing formulas and thus, require a larger amount of computation time. If we have several processors, then, it is desirable to perform these algorithms in parallel on several processors, and thus, to speed up computations. In this paper, we show how the algorithms for estimating variance under interval and fuzzy uncertainty can be parallelized.