This paper is concerned with the estimation of the volume fraction and the anisotropy of a two-component composite from measured bulk properties. An algorithm that takes into account that measurements have errors is developed. This algorithm is used to study data from experimental measurements with an unknown microstructure. The dependence on the microstructure is quantified in terms of a measure in the representation formula introduced by D. Bergman. We use composites with known microstructures to illustrate the dependence on the underlying measure and show how errors in the measurements affect the estimations of the structural parameters