There's an old story about the statistician who drowned after seeing that the average depth was 3ft. Averages, or in this case the mean, necessarily hide some data, but very often they also hide what's really going on.
Let's say you run a delivery service and have an average delivery time of one day, it could be that most deliveries are actually a few hours while a few particular ones have people waiting for a week. Or a figure of average incomes might hide that most people have low salaries and a few are millionaires. But just looking at the average you can't tell. Sometimes a different measure of central tendency, like the median, can provide a clearer picture.
Sheldon Zedeck, a UC Berkeley psychology professor who taught me about the design of experiments, gave wise advice: spend time with your data. Sometimes it's the only way to know what's happening for sure.