If you have access to a licence, MATLAB is great for this type of work, and there is an extensive user community who share scripts and advice. I have not used "R" extensively, but it is free and appears to enjoy many of the benefits of MATLAB.
You can use excel capabilities which can do simple statistical analysis. You can use many free statistical open source free software according to your needs. For example see the link:
Piper software is a free software to prepare Piper diagram. Since hydrological data are multivariate, common software like SPSS, Statistica are also useful.
Hydrological data is multivariate in nature. Univariate statistics like computation of minimum and maximum values, mean, mode, median, standard deviation, skewness and kurtosis; trend-surface analysis; bivariate statistics like correlation and regression analysis; multivariate statistics like multiple regression, cluster analysis and principal component analysis can be done from groundwater data. These analyses (excluding trend-surface analysis) can be done by very common software like MS Excel and SPSS. Specific plots like Piper diagram can be done by specific software, some of which are free and others are to be purchased.