1 Introduction -- 2 Vague Data -- 3 Fuzzy Sets of the Real Line -- 4 Operations on Fuzzy Sets -- 4.1 Set Theoretical Operations -- 4.2 On Zadeh's Extension Principle -- 4.3 Arithmetic Operations -- 5 Representation of Vague Data in a Digital Computer -- 6 Topological Properties of Fuzzy Set Spaces -- 7 Random Sets and Fuzzy Random Variables -- 8 Descriptive Statistics with Vague Data -- 8.1 Expected Value -- 8.2 Variance -- 8.3 Empirical Distribution Function -- 9 Distribution Functions and i.i.d.-Sequences of Random Variables -- 10 Limit Theorems -- 10.1 Strong Law of Large Numbers -- 10.2 Consistent Estimators in the Finite Case -- 10.3 Gliwenko-Cantelli Theorem -- 10.4 Related Results -- 11 Some Aspects of Statistical Inference -- 11.1 Parametric Point Estimation -- 11.2 Confidence Estimation -- 11.3 The Testing of Hypotheses -- 12 On a Software Tool for Statistics with Vague Data -- 12.1 Linguistic Modelling -- 12.2 Linguistic Approximation -- 12.3 Examples -- References -- List of Symbols.