Percentiles and Box Plots · Superchallenge problem

A data set of eight numbers has five-number summary $2, 4, 7, 11, 15$ (minimum, $Q_1$, median, $Q_3$, maximum), where $Q_1$ and $Q_3$ are the medians of the lower four and upper four values. The individual values are not given. Find the mean of the data set.