Detailed studies of the resolution of a EUDET-type beam telescope are carried out using the DATURA beam telescope as an example. The EUDET-type beam telescopes make use of CMOS MIMOSA 26 pixel detectors for particle tracking allowing for precise characterisation of particle sensing devices. A profound understanding of the performance of the beam telescope as a whole is obtained by a detailed characterisation of the sensors themselves. The differential intrinsic resolution as measured in a MIMOSA 26 sensor is extracted using an iterative pull method and various quantities that depend on the size of the cluster are discussed: the residual distribution, the intra-pixel residual-width distribution and the intra-pixel density distribution of track incident positions.