The mean deviation of a set of values from their mean is calculated by finding the average of the absolute differences between each value and the mean.

Given the values \(x\), \(2x\), \(x+1\), and \(3x\) with a mean of 2, we can set up the equation for the mean:

Mean = \(\frac{x + 2x + x + 1 + 3x}{4} = \frac{7x + 1}{4} = 2\)

Solve for \(x\):

\(7x + 1 = 8\)

\(7x = 7\)

\(x = 1\)

Substitute \(x = 1\) back into the values to find the set: \(1\), \(2\), \(2\), and \(3\).

Now, calculate the mean deviation:

Mean Deviation = \(\frac{|1 - 2| + |2 - 2| + |2 - 2| + |3 - 2|}{4} = \frac{1 + 0 + 0 + 1}{4} = \frac{2}{4} = 0.5\)

So, the mean deviation is 0.5.