Step 1 :Calculate the mean of the given data set: \(\frac{2.4 + 1.6 + 3.2 + 0.3 + 1.5}{5} = \boxed{1.8}\)
Step 2 :Add 10 to each data point: \(12.4, 11.6, 13.2, 10.3, 11.5\)
Step 3 :Calculate the new mean: \(\frac{12.4 + 11.6 + 13.2 + 10.3 + 11.5}{5} = \boxed{11.8}\)
Step 4 :Double each new data point: \(24.8, 23.2, 26.4, 20.6, 23.0\)
Step 5 :Calculate the final mean: \(\frac{24.8 + 23.2 + 26.4 + 20.6 + 23.0}{5} = \boxed{23.6}\)