Calculate the Mean of Four Identical Mixed Numbers: 10½

To solve this problem, we need to find the average of four identical numbers: $10\frac{1}{2}$. We will follow these steps:

• Step 1: Recognize that the problem involves calculating the average of identical numbers.
• Step 2: Choose to convert the mixed number $10\frac{1}{2}$ into a more convenient form, such as a decimal or improper fraction.
• Step 3: Compute the sum of these numbers and divide by the total number of terms.

Let's proceed with these steps:
Step 1: Each number is the same, $10\frac{1}{2}$. A mixed number like $10\frac{1}{2}$ can either be expressed as $10.5$ (decimal form) or as the improper fraction $\frac{21}{2}$.
Step 2: There are four numbers, each valued at $10.5$. The sum of these numbers is $4 \times 10.5 = 42$.
Step 3: Divide this sum by the number of numbers (4):
$\text{Average} = \frac{42}{4} = 10.5$

Therefore, the average of the numbers $10\frac{1}{2}, 10\frac{1}{2}, 10\frac{1}{2},$ and $10\frac{1}{2}$ is $10\frac{1}{2}$.