Five waiting times
Suppose five people in a fictional service wait 2, 3, 4, 5, and 36 days. The total is 50 days, so the mean is 10 days. The median is 4 days.
“The average wait was ten days” and “half waited no more than four days” describe different features of the same group. The long wait strongly affects the mean. The median gives less information about that tail.
Now replace 36 with 6. The median remains four, but the mean falls to four. A service could therefore improve its longest waits substantially without changing its median.
Which number is better?
That depends on the question. If planning total waiting-related workload, the mean and distribution may be relevant. If describing the middle person's experience, the median may be more intuitive. If assessing whether some people face unacceptable delays, an upper percentile or the proportion exceeding a stated threshold can matter more than either average.
The NIST statistical handbook describes measures of location and spread. The useful principle is to choose a summary that matches the question, rather than naming one average as inherently honest and the other misleading.
Read beyond the center
For a study result, look for sample size, spread, and a graph when available. A mean improvement can combine large gains for some people, little change for others, and deterioration for a few.
The numbers above are an arithmetic example, not a model of a particular healthcare service. They show why a seemingly simple comparison between two averages can conceal a meaningful difference in who waits longest. An average is a summary of a group, not a promise to an individual.
