If x is the mean of data 3, x, 2 and 4, then the mode is _______

The correct answer is 3.

Let us find the value of $x$ first, and then determine the mode of the given data set.

We are given that $x$ is the mean of the data set: 3, $x$, 2, and 4.
The number of data points (observations) is 4.
The formula for the mean is the sum of all observations divided by the total number of observations:
$\mathrm{Mean}=\frac{3+x+2+4}{4}$

Since the mean is equal to $x$, we can write the equation:
$x=\frac{9+x}{4}$

To solve for $x$, we multiply both sides of the equation by 4:
$4x=9+x$

Subtracting $x$ from both sides gives:
$3x=9$

Dividing both sides by 3, we find:
$x=3$

Now that we have $x=3$, we can substitute this value back into the original data set.
The numbers in the data set are: 3, 3, 2, and 4.

The mode is the value that appears most frequently in a data set.
In our data set {3, 3, 2, 4}:
- The number 3 appears twice.
- The number 2 appears once.
- The number 4 appears once.
Since the value 3 repeats the maximum number of times, the mode of the data is 3.