Two data sets, C and D, of $23$ integers each are summarized in the histograms shown. For each histogram, the first interval represents the frequency of integers greater than or equal to its starting value but less than its ending value (e.g., for Data Set C, $\ge 10$ and $<20$). The second interval follows similarly, and so on. What is the largest possible difference between the mean of data set D and the mean of data set C?