Given the statistical data set \(\{3x+2, 4x-3, 5x+1, 6x-5\}\), where x is a positive integer, find the mean (average) of the data set after factoring by grouping.

Step 1 ：Step 1: Calculate the sum. \(\sum = (3x+2) + (4x-3) + (5x+1) + (6x-5) = 18x - 5\)

Step 2 ：Step 2: Factor by grouping. \(18x - 5 = 18(x - \frac{5}{18})\)

Step 3 ：Step 3: Calculate the mean. \(\text{Mean} = \frac{\text{Sum}}{\text{Total number of data}} = \frac{18(x - \frac{5}{18})}{4} = \frac{9}{2}(x - \frac{5}{18})\)