Statistics tools available in Debian.

Environments to explore and model data

The R statistical software, is an environment to explore and model statistical data, based on the R programming language upstream. Debian includes almost 1000 r-cran packages for specialized analysis. There are frontend GUIs for R available including Rkward, RCommander, Littler and Cantor.
GNU PSPP software, is a familiar spreadsheet-like environment to view and test statistical data upstream.
LibreOffice Calc, is a spreadsheet that includes dozens of functions and several guis for hypothesis testing and distribution modeling upstream.
Gnumeric, is a spreadsheet that includes functions for hypothesis testing and data modeling upstream. There are also extensions through which Perl and Python statistical functions (see below) can be called.
Ministat software, provides a simple statistical analysis of datasets.
Datamash, performs basic numeric, textual and statistical operations on textual data files.
Octave statistics, is a module providing statistical functions within the scientific modeling language GNU Octave upstream.
JAGS software, provides a sophisticated analysis of Bayesian hierarchical models upstream.

Scipy is a group of scientific modules built around the python programming language upstream. It contains among others the numpy, matplotlib and pandas. There are also python modules specifically for statistical data processing such as bayespy, bumps, patsy, seaborn and statsmodels.
libghc-statistics provides statistical functions to the Haskell programming language upstream.
ruby-statistics and ruby-enumerable-statistics are two gems that provides the programming language ruby with statistical capabilities upstream.
The Perl programming language is well-supplied with several statistics modules including libstatistics-descriptive-perl, libstatistics-distributions-perl, libstatistics-lite-perl, libstatistics-contingency-perl, libpdl-stats-perl, and libstatistics-r-perl upstream.
libjs-sciencejs provides statistical functions in the science.stats module to the Javascript programming language upstream.
libdistlib-java and libcommons-math3-java are two modules that provides the programming language java with statistical capabilities upstream.

Apophenia statistical C library, is a C library for statistics. upstream.
Boost C++ math library, is a C++ library including statistical functions. upstream.
Oakleaf Robust Statistics, is a C library for computing robust statistical estimates.
TAMU ANOVA, is a one and two way ANOVA library in C.

Emacs Speaks Statistics (ESS), Emacs mode for statistical programming and data analysis.
Geany, fast and lightweight IDE that speaks R and most of the other languages above.
Neovim and Vim, have a plugin that works with R code.
Rkward includes an IDE (a subset of Kate) alongside its R GUI.

Packages being worked on
Jamovi, an SPSS-like statistics package with a spreadsheet editor and R support upstream.
pymc3, Bayesian statistical modeling and probabilistic machine learning software.
R Studio, is the most popular GUI front end for R. upstream
JASP is another SPSS-like statistics package with a spreadsheet editor and R support.
Rattle, is another popular, lightweight GUI front end for R aimed at data science.