the median of 10, 14, 11, 9, 8, 12, 6 is

Options

A. 14
B. 11
C. 10
D. 12

Answer

To find the median of the given set of numbers (10, 14, 11, 9, 8, 12, 6), we can follow these steps:

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

- The given numbers are: 10, 14, 11, 9, 8, 12, 6
- Arranging them in ascending order gives us: 6, 8, 9, 10, 11, 12, 14

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

- The sorted data has 7 numbers: 6, 8, 9, 10, 11, 12, 14

### Step 3: Determine if the count is odd or even
Since there are 7 numbers, we note that the count is odd.

### Step 4: Use the median formula for an odd number of observations
For a dataset with an odd number of observations, the median is found using the formula:
\[ \text{Median} = \frac{n + 1}{2} \text{th term} \]
where \( n \) is the number of observations.

- Here, \( n = 7 \)
- Thus, we calculate:
\[ \text{Median} = \frac{7 + 1}{2} = \frac{8}{2} = 4 \]

### Step 5: Identify the 4th term in the sorted data
Now, we need to find the 4th term in our sorted list.

- The sorted list is: 6, 8, 9, 10, 11, 12, 14
- The 4th term is 10.

### Conclusion
Therefore, the median of the given numbers is **10**.

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