The possibilities of using various methods of mathematical statistics for processing and analyzing the results of deformation and strength tests on composites made from a low-density polyethylene and linen yarn production waste are evaluated. The hypothesis that the experimental strength data agree with the Gaussian distribution is examined by the Shapiro–Wilk test (W-test.) It is shown that the Gaussian distribution, both for systems unmodified and modified with diphenylmethane diisocyanate (DIC), is valid only for two parameters: the maximum tensile strength σmax and the elastic modulus E t. For the other parameters (the relative elongation εmax corresponding to σmax, the specific total work of failure A b), and the specific work of failure to the tensile strength A max), a non-Gaussian distribution is observed. An analysis of measurements for different specimens by the Bartlett test shows that the E t data have equal variances for both systems (with and without DIC), but for the system containing DIC, the σmax data have different variances. A two-factor ANOVA analysis reveals that DIC considerably affects the tensile strength and modulus of composites, but the influence of test conditions is a statistically significant factor only for the modulus. The coefficient of variation is considerably lower for σmax than for E t and can be used as a quantitative measure for the degree of heterogeneity of the composites investigated.