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The mean of the data set is the sum of all the numbers divided by the total number of values.
Sum of the numbers in the data set: 23 + 32 + 38 + 19 + 28 + 27 + 18 + 36 + 29 + 26 + 32 = 308
Total number of values in the data set: 11
Mean = Sum of values / Total number of values = 308 / 11 = 28
Therefore, the mean of the data set is 28. Answer: \boxed{28}.