How do you find the median of an even number of data points?

To find the median of a dataset containing an even number of data points, you calculate the average of the two middle numbers.

Here's a breakdown:

1. Order the data: First, arrange the numbers in ascending order (from smallest to largest).

2. Identify the middle numbers: With an even number of data points (let's say 'n' data points), the two middle numbers are the (n/2)th number and the (n/2 + 1)th number.

3. Calculate the average: Add the two middle numbers together and divide by 2. This average is the median.

Formula:

Median = ((n/2)th observation + (n/2 + 1)th observation) / 2

Example:

Consider the following dataset: 4, 2, 8, 6, 10, 12

1. Order the data: 2, 4, 6, 8, 10, 12
2. Identify the middle numbers: There are 6 numbers (n=6), so the middle numbers are the (6/2)th = 3rd number and the (6/2 + 1)th = 4th number. These are 6 and 8.
3. Calculate the average: (6 + 8) / 2 = 7

Therefore, the median of the dataset is 7.

Why this works:

The median represents the "middle" value of a dataset. When you have an even number of data points, there isn't a single middle value. By averaging the two closest to the center, we determine a point that equally divides the data, fulfilling the definition of the median.