Tensile strengths of small-diameter ceramic fibers are commonly obtained from measured fracture loads on individual fibers and the average cross-sectional area of the entire fiber population. The goal of the present article is to provide a critical assessment of the consequences of using the average fiber area in the inferred strength distribution. The issues are addressed through established theorems in convolution and uncertainty propagation as well as Monte Carlo simulations. Systematic errors introduced by using the average area are well-represented by simple analytical formulae. The formulae are couched in terms of the coefficient of variation in fiber area and the dispersion in fiber strengths, characterized by the Weibull modulus. In turn, the formulae are used to determine the true values of Weibull modulus and reference strength from their nominal values. Random uncertainties associated with a finite number of tests decay slowly with number, in accordance with an inverse root scaling. When systematic errors are conflated with random uncertainties, accurate determination of the true Weibull modulus becomes increasingly challenging, even for seemingly large numbers of strength measurements. The results are used to assess the fidelity of previously-reported experimental results based on nominal strength data.