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 numbers 10, 14, 11, 9, 8, 12, and 6, follow these steps:

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

The 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 total number of observations.
Next, we count how many numbers we have in total.

The total numbers are:
1. 6
2. 8
3. 9
4. 10
5. 11
6. 12
7. 14

There are 7 numbers in total.

### Step 3: Determine if the total number of observations is odd or even.
Since the total number of observations (7) is odd, we will use the formula for finding the median for an odd number of observations.

### Step 4: Use the median formula for an odd number of observations.
The formula to find the median when the number of observations (n) is odd is:
\[ \text{Median} = \frac{n + 1}{2} \]

Substituting the value of n:
\[ \text{Median} = \frac{7 + 1}{2} = \frac{8}{2} = 4 \]

### Step 5: Find the 4th term in the arranged list.
Now, we locate the 4th term in our sorted list:
1. 1st term: 6
2. 2nd term: 8
3. 3rd term: 9
4. 4th term: 10

Thus, the median is the 4th term, which is 10.

### Conclusion:
The median of the numbers 10, 14, 11, 9, 8, 12, and 6 is **10**.

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