When the Average Lies

Mean, median, and mode can lead to very different interpretations of the same data, often producing conflicting summaries.

After the CSAT, the results became the main topic of discussion. People evaluated the difficulty of the exam using raw scores, rankings, and average scores. At the time, I accepted these numbers without much doubt. The average, in particular, appeared simple and reliable, as if it could explain everything on its own.

My perspective changed when I later reviewed the score data independently. Most test scores were clustered within a relatively narrow range, which matched my memory of how the exam room felt during the test. However, a small number of students achieved extremely high scores. Although they represented only a small portion of the student body, their scores raised the average noticeably. As a result, the average no longer reflected how most students actually performed.

This was when I began to understand the limitations of the mean. Because averages are sensitive to extreme values, they can distort the overall picture. In contrast, the median and the mode showed where the majority of students were truly positioned. Looking at percentiles also helped explain why students with nearly identical scores could end up in different rankings.

This pattern extends beyond exam results. Average income and average housing prices can also be misleading when a small number of extreme values dominate the data. That is why distributions matter more than any single number. Learning to look beyond averages and focus on distributions has changed how I understand statistics—and how I interpret numbers in everyday life.