To find the median of the given numbers: 12, 10, 5, 31, 89, 42, and 11, we will follow these steps:
### Step 1: Arrange the numbers in ascending order.
First, we need to sort the numbers from the smallest to the largest.
- The given numbers are: 12, 10, 5, 31, 89, 42, 11.
- Arranging them in ascending order gives us: 5, 10, 11, 12, 31, 42, 89.
### Step 2: Determine the number of values (n).
Next, we count how many numbers we have.
- The sorted list is: 5, 10, 11, 12, 31, 42, 89.
- There are a total of 7 numbers (n = 7).
### Step 3: Use the median formula for an odd number of observations.
Since the number of observations (n) is odd, we use the formula for the median:
\[
\text{Median} = \left( \frac{n + 1}{2} \right)^{th} \text{ term}
\]
Substituting n = 7 into the formula:
\[
\text{Median} = \left( \frac{7 + 1}{2} \right)^{th} \text{ term} = \left( \frac{8}{2} \right)^{th} \text{ term} = 4^{th} \text{ term}
\]
### Step 4: Identify the 4th term in the sorted list.
Now, we need to find the 4th term in our sorted list.
- The sorted list is: 5, 10, 11, 12, 31, 42, 89.
- The 4th term is 12.
### Conclusion:
Thus, the median of the given numbers is **12**.
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