The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is ?35552545

1. Break Down the Problem

To find the excluded number, we need to calculate the total of the five numbers and then compare it to the total when one number is excluded.

2. Relevant Concepts

• Average Formula: The average of a set of numbers is given by the formula: $\text{Average} = \frac{\text{Sum of all numbers}}{\text{Count of numbers}}$

3. Analysis and Detail

1. Let the five numbers be represented as $x_1, x_2, x_3, x_4, x_5$.

2. The average of these five numbers is 27: $\frac{x_1 + x_2 + x_3 + x_4 + x_5}{5} = 27$ Hence, the sum of the five numbers is: $x_1 + x_2 + x_3 + x_4 + x_5 = 27 \times 5 = 135$

3. When one number is excluded (let's denote the excluded number as $x_e$), the average of the remaining four numbers becomes 25: $\frac{x_1 + x_2 + x_3 + x_4}{4} = 25$ Therefore, the sum of the remaining four numbers is: $x_1 + x_2 + x_3 + x_4 = 25 \times 4 = 100$

4. Using the equations derived: $x_1 + x_2 + x_3 + x_4 + x_e = 135$ and $x_1 + x_2 + x_3 + x_4 = 100$ We can substitute the second equation into the first: $100 + x_e = 135$

4. Verify and Summarize

Now, we solve for $x_e$: $x_e = 135 - 100 = 35$

Final Answer

The excluded number is $\boxed{35}$.