We present the TüEyeQ data set - to the best of our knowledge - the most comprehensive data set generated on a culture fair intelligence test (CFT 20-R), i.e., an IQ Test, consisting of 56 single tasks, taken by 315 individuals aged between 18 and 30 years. In addition to socio-demographic and educational information, the data set also includes the eye movements of the individuals while taking the IQ test. Along with distributional information we also highlight the potential for predictive analysis on the TüEyeQ data set and report the most important covariates for predicting the performance of a participant on a given task along with their influence on the prediction.