To find the mean deviation of the data set \(2, 4, 4, 7, 8\), follow these steps:

1. Find the mean of the data set:

\[
\text{Mean} = \frac{2 + 4 + 4 + 7 + 8}{5} = \frac{25}{5} = 5
\]

2. Calculate the absolute deviations from the mean:

\[
|2 - 5| = 3
\]
\[
|4 - 5| = 1
\]
\[
|4 - 5| = 1
\]
\[
|7 - 5| = 2
\]
\[
|8 - 5| = 3
\]

3. Find the mean of these absolute deviations:

\[
\text{Mean deviation} = \frac{3 + 1 + 1 + 2 + 3}{5} = \frac{10}{5} = 2
\]

So, the mean deviation of the data set is 2, which corresponds to option A.