Step 1 :Calculate the mean and median of the current set: \(data = [3, 4, 4, 6]\), \(mean = 4.25\), \(median = 4.0\)
Step 2 :Let x be the number we need to add to the set. The new mean will be \((sum\ of\ the\ set + x) / 5\) and the new median will be the middle number of the sorted set.
Step 3 :Set up an equation and solve for x: \(\frac{x}{5} + \frac{17}{5} = \frac{x}{2} + 2\)
Step 4 :Solve for x: \(x = \frac{14}{3}\)
Step 5 :\(\boxed{\text{The number to add to the set is }\frac{14}{3}}\)