Functional principal components analysis on the example of the achievements of students in the years 2009-2017

The functional principal components analysis joins the advantages of the principal components analysis and provide analysis of dynamic data. The main difference in both methods is the type of data the PCA is based on multivariate data, whereas the FPCA on the functional data including curves and trajectories, i.e. a series of individual observations, not a single observation, as usual. The functional principal components analysis with functional data, will be used in the analysis. This method allows the analysis of dynamic data. The purpose of the article is to apply of functional principal components analysis to the problem of student’s achievements. The article was compared the level of students' knowledge during different stages of education in 2009-2017. The analysis covers the average exam results after the II, III and IV stage of education.