The median of 8 numbers is 11. If 7 of these numbers are 26, 12, 3, 8, 5, 20, and 14, find the eighth number.

Options

A. `11`
B. `8`
C. `10`
D. `9`

Answer

To find the eighth number when the median of eight numbers is given as 11, and seven of these numbers are provided, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The median of the eight numbers is 11.
- The seven known numbers are: 26, 12, 3, 8, 5, 20, and 14.

2. **Arrange the Known Numbers in Ascending Order**:
- Sorting the numbers: 3, 5, 8, 12, 14, 20, 26.

3. **Determine the Position of the Eighth Number**:
- Since we have 8 numbers, the median is calculated as the average of the 4th and 5th numbers in the sorted list.
- We denote the eighth number as \( x \).

4. **Insert the Eighth Number in the Sorted List**:
- The sorted list with the eighth number \( x \) will be: 3, 5, 8, \( x \), 12, 14, 20, 26.
- We need to find the value of \( x \) such that the median (average of the 4th and 5th terms) equals 11.

5. **Set Up the Median Equation**:
- The 4th term is \( x \) and the 5th term is 12.
- The formula for the median is:
\[ \text{Median} = \frac{\text{4th term} + \text{5th term}}{2} \]
- Plugging in the values we have:
\[ 11 = \frac{x + 12}{2} \]

6. **Solve for \( x \)**:
- Multiply both sides by 2:
\[ 22 = x + 12 \]
- Subtract 12 from both sides:
\[ x = 10 \]

7. **Conclusion**:
- The eighth number is \( x = 10 \).

### Final Answer:
The eighth number is **10**.