Given,

The mean of five numbers = 30

Now to calculate the sum of these five numbers we have to multiply the mean by 5,

So, we get,

Sum of five numbers = 5 × 30 = 150

Change in the mean when one number is excluded, it become = 28

Sum of remaining four numbers = 4 × 28 = 112

Now to find out the excluded number we have to subtract the sum of four numbers from the sum of five numbers,

We get,

The excluded number = sum of five numbers - sum of four numbers

= 150 – 112 = 38