To find the mean of the given data, you need to add up all the values and then divide by the number of values.

The data is: \(t, 2t-1, t-2, 2t - 1, 4t, 2t+2\)

Sum of the values = \(t + (2t-1) + (t-2) + (2t - 1) + 4t + (2t+2)\)

= \(12t - 2\)

Number of values = 6

Mean = Sum of values / Number of values

Mean = \(\frac{12t - 2}{6}\)

Mean = \(2t - \frac{1}{3}\)

So, the mean of the data is \(2t - \frac{1}{3}}\).