Two data sets of $23$ integers each are summarized in the histograms shown. For each of the histograms, the first interval represents the frequency of integers greater than or equal to $10$, but less than $20$. The second interval represents the frequency of integers greater than or equal to $20$, but less than $30$, and so on. What is the largest possible difference between the mean of data set A and the mean of data set B?