Data privacy studies methods to ensure that disclosure of sensitive information does not take place. Masking methods are applied to databases prior to their release so that intruders cannot access sensitive information. Masking methods modify the data reducing its quality. Information loss measures have been defined to evaluate in what extent data is still useful for particular analysis. In the case of big data, masking data and evaluating its utility is a complex problem. In this paper we focus on information loss measurement and we explore if we can estimate or give bounds of information loss for large data sets using only random subsets of the whole data set.