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Abstract: [Truncated] The central aim of the thesis is to investigate and present results of studies of two geometrical methods of inference: the measure of central tendency in Riemannian manifolds - the Riemannian mean and; the interpolation of data points in Riemannian manifolds - the Riemannian variational curves. Riemannian manifolds are smooth spaces equipped with a metric allowing to measure geometric quantities like distances and angles. Riemannian geometry ­ the branch of differential geometry concerning Riemannian manifolds - evolved from Euclid's plane and solid geometry, and from Gauss's theory of curved spaces. The thesis develops a geometrical approach to investigations of data in Riemannian manifolds.