To find the median of a set of numbers, you need to follow these steps:
- Organize the numbers in ascending order.
- Identify the middle number(s).
- Calculate the median based on whether there is an odd or even number of observations.
Let's go through these steps with the numbers you provided: \(2, 6, 9, 5, 2, 41, 8\).
Step 1: Organize in Ascending Order
First, let's sort the numbers:
- The sorted order is: \(2, 2, 5, 6, 8, 9, 41\)
Step 2: Identify the Middle Number
Now, we need to count how many numbers we have:
- There are 7 numbers in total (which is odd).
Step 3: Calculate the Median
For an odd set of numbers, the median is the middle number. The middle number can be found using the formula: \[ \text{Median index} = \frac{n + 1}{2} \] where \(n\) is the number of observations.
In our case: \[ \text{Median index} = \frac{7 + 1}{2} = \frac{8}{2} = 4 \]
The 4th number in the sorted list is:
- \(2, 2, 5, \mathbf{6}, 8, 9, 41\)
Therefore, the median is: \[ \boxed{6} \]