For a probability space (Ω * , A,]P), ar r.v. X : Ω * → R and random samplesX 1 (ω), X 2 , ,X n with one vague data associated with p.d.f.f(x θ), we tried to define sufficient statistic and unbiased estimator for them, and also to test simple and likelihood ratio hypotheses with one vague data. We have shown in our examples that using all the data (including the vague data), we can have the same result as using the n -- 1 stable data to test the hypotheses in crisp statistics. Alternatively, if the result of our study can be generalized to several vague data, it can be seen that we may not need to determine the outliers from our statistical data in the future.