Measurements of single electron tunneling through a quantum dot (QD) using a quantum point contact as charge detector have been performed for very long time traces with very large event counts. This large statistical basis is used for a detailed examination of the counting statistics for varying symmetry of the QD system. From the measured statistics we extract high order cumulants describing the distribution. Oscillations of the high order cumulants are observed when varying the symmetry. We compare this behavior to the observed oscillation in time dependence and show that the variation in both system variables lead to the same kind of oscillating response. © 2010 American Institute of Physics.