What is the median of these numbers

2,6,9,5,2,41,8
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1 answer

To find the median of a set of numbers, you need to follow these steps:

  1. Organize the numbers in ascending order.
  2. Identify the middle number(s).
  3. 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: \[ \boxed{6} \]