If the median of the set {2, 4, x, 6} is 4, what is the value of x?

To determine the value of ( x ) such that the median of the set {2, 4, x, 6} is 4, it is essential to understand how the median is calculated. The median is the middle value of a sorted list of numbers. If there is an even number of values, the median is the average of the two middle numbers.

First, let's consider the possible scenarios for the value of ( x ):

1. If ( x ) is less than or equal to 2, the sorted set would be {x, 2, 4, 6}. The middle numbers would be 2 and 4. In this case, the median would be ( \frac{2 + 4}{2} = 3 ), which is not 4.

2. If ( x ) equals 4, the sorted set will be {2, 4, 4, 6}. Here, the middle numbers are 4 and 4, leading to a median of ( \frac{4 + 4}{2} = 4 ). This matches the condition given in the question.

3. If ( x ) is greater than 4 but less than or