The median of eight numbers is 45. Given that seven of the numbers are 9, 2, 3, 4, 12, 13 and 1, find the eighth number.

To find the eighth number, let's first understand that the median of eight numbers is the average of the 4th and 5th numbers when they are arranged in ascending order. Since we know the median is 45, the sum of the 4th and 5th numbers must be \(2 \times 45 = 90\).

### Step-by-step Solution:

1. **Arrange the Given Numbers in Ascending Order**:  
   The seven given numbers are: 9, 2, 3, 4, 12, 13, 1.  
   Arranging them in ascending order, we get:  
   \[
   1, 2, 3, 4, 9, 12, 13
   \]

2. **Identify the Position of the Median**:  
   The median is the average of the 4th and 5th numbers in the sorted list. If we add the eighth number (let's call it \(x\)), the list in ascending order will have the numbers at these positions:

   \[
   1, 2, 3, 4, ?, ?, ?, ?
   \]

   The 4th and 5th positions are the two middle numbers.

3. **Determine Where \(x\) Should Be Placed**:  
   The 4th and 5th numbers need to sum up to 90. We already have the first four numbers as 1, 2, 3, and 4. For the median to be 45, we need to determine where \(x\) should fit.

4. **Calculate the Value of \(x\)**:  
   If \(x\) is larger than 9, then the 4th number will still be 4, and the 5th number will be \(x\). The median condition tells us:

   \[
   4 + x = 90
   \]

   Solving for \(x\):

   \[
   x = 90 - 4 = 86
   \]

### Conclusion:
The eighth number is **86**.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the difference between the mean and median of a dataset?
2. How do you find the median for an odd number of elements?
3. Can you explain how the median is different from the mode?
4. How do you calculate the mean, median, and mode in a larger dataset?
5. What happens to the median if an extreme outlier is added to the dataset?

**Tip**: When solving median problems, always remember to arrange the numbers in ascending order first.

The median of eight numbers is 45. Given that seven of the numbers are 9, 2, 3, 4, 12, 13, and 1, find the eighth number.

Learn how to calculate the eighth number in a set where the median of eight numbers is given as 45. This problem involves ordering data and applying the median formula, making it ideal for students in Grades 6-8. Explore the step-by-step solution and improve your understanding of median calculations.

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