Certified Advanced Alcohol and Drug Counselor (CAADC) Practice Exam

How do you find the median of a set with an even number of items?

1. A set with an even number of items does not have a median

2. Find the average of the two middle numbers

3. The two middle numbers are both medians

4. The larger of the two middle numbers is the median

The correct answer is: Find the average of the two middle numbers

To determine the median of a set containing an even number of items, the correct approach is to find the average of the two middle numbers. When the dataset is organized in ascending order, the median is defined as the point that divides the dataset into two equal halves. For an even-numbered set, there isn't a single middle number; instead, there are two middle numbers that lie at the center of the ordered list. Calculating the average of these two numbers accurately reflects the central tendency of the entire set, ensuring that the computed median remains a representative value. The understanding that the two middle numbers must be averaged rather than chosen individually as a median emphasizes the concept that the median must lie exactly in the center of the dataset, rather than being simply the larger, smaller, or non-existent when two numbers occupy that central position. This method ensures statistical accuracy and fidelity to the definition of the median in mathematical terms.