W and Z bosons are the mediators of the fundamental weak force and are some of the particles produced using proton-proton collisions with the Large Hadron Collider at CERN. Proton-proton interactions producing Z bosons, which subsequently decay into leptonic particles, like electrons, are known as the Drell-Yan process. Its differential cross-section expresses the probability for this process to occur depending on the Z bosons' and decay products' kinematic variables. It can be separated into eight spin-related ratios, known as the Drell-Yan angular coefficients. This thesis is a feasibility study to explore if there is sufficient statistical sensitivity to measure the coefficients with special data sets. Taken with the ATLAS detector, these sets have a lower average number of interactions per proton bunch crossing. This thesis includes predictions of the coefficients and comparisons of MC simulations to the data; this is the first look at these data sets.