To find the variance of a set of data points, we need to follow these steps:

1. Find the mean (\(\mu\)) of the data set.

2. Calculate the squared differences between each data point and the mean.

3. Find the mean of the squared differences (this is the variance).

Let's work through the problem step by step.

The data set is: \(2x\), \(2x-1\), \(2x+1\).

Step 1: Find the mean (\(\mu\)) of the data set.

\[

\mu = \frac{(2x) + (2x-1) + (2x+1)}{3} = \frac{6x}{3} = 2x

\]

Step 2: Calculate the squared differences between each data point and the mean.

For \(2x\):

\[

(2x - 2x)^2 = 0

\]

For \(2x-1\):

\[

(2x-1 - 2x)^2 = (-1)^2 = 1

\]

For \(2x+1\):

\[

(2x+1 - 2x)^2 = 1

\]

Step 3: Find the mean of the squared differences (this is the variance).

\[

\text{Variance} = \frac{0 + 1 + 1}{3} = \frac{2}{3}

\]