The development of statistical literacy has become a key outcome of mathematics curricula in various countries. The purpose of the study was to explore primary pre-service teachers' (PSTs') knowledge of aspects of measures of central tendency, which is a central concept in statistical literacy. The 183 PSTs' written responses to four tasks were analysed in terms of demands elucidated by the Mathematical Knowledge for Teaching (MKT) framework. The results showed that almost all the participants were able to carry out simple computations of the mean and median and were generally able to identify learner errors. However, they found it much harder to solve problems that required unpacking of the procedures and comparison of different measures of central tendency. They also struggled with providing suitable feedback based on learner errors. This study shows that primary school PSTs need more support in developing these MKT skills with respect to the concepts of the mean and median.