Find the median of the data 9, 12, 11, 10, 8, 9, 11.

Options

A. 9
B. 10
C. 11
D. 12

Answer

To find the median of the data set 9, 12, 11, 10, 8, 9, 11, we will follow these steps:

### Step 1: Arrange the data in ascending order.
First, we need to sort the numbers from smallest to largest.

- The original data is: 9, 12, 11, 10, 8, 9, 11.
- Arranging these in ascending order gives us: 8, 9, 9, 10, 11, 11, 12.

### Step 2: Count the number of observations.
Next, we count how many numbers are in our sorted list.

- The sorted data is: 8, 9, 9, 10, 11, 11, 12.
- There are 7 numbers in total.

### Step 3: Determine if the number of observations is odd or even.
Since we have 7 observations, which is an odd number, we will use the formula for finding the median in an odd set.

### Step 4: Calculate the position of the median.
For an odd number of observations, the median is found at the position given by the formula:
\[ \text{Median Position} = \frac{n + 1}{2} \]
where \( n \) is the number of observations.

- Here, \( n = 7 \).
- So, the median position is:
\[ \frac{7 + 1}{2} = \frac{8}{2} = 4 \]

### Step 5: Find the median value.
Now, we find the value at the 4th position in our sorted list.

- The sorted data is: 8, 9, 9, 10, 11, 11, 12.
- The 4th number in this list is 10.

### Conclusion:
Thus, the median of the data set 9, 12, 11, 10, 8, 9, 11 is **10**.

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