Skewed data and the long tail
The bell is symmetric. But plenty of real data is lopsided: most values are small, with a long tail of rare large ones stretching right. Remember the salaries with the director from part one โ that is exactly this case. Drag the skewness slider and watch the mean, median and mode drift apart.
Skewness is asymmetry: one tail is longer than the other. Push the slider right โ a long tail stretches right (right skew); left โ the opposite. On a symmetric distribution (slider centered) the mean, median and mode coincide. As soon as a tail appears, they drift apart.
What it means
Incomes, housing prices, session durations, city sizes โ almost always right-skewed. Their mean is inflated by the tail, and the median is more honest.
You must recognize the shape before the analysis: skew changes which measures and methods are even allowed.
Where it shows up
Service response time is a classic long tail: almost all requests are fast, but rare slow ones pull the mean up. That is why engineers watch the median and the tail percentiles (95th, 99th), not the mean.
Wealth in society works the same way: the mean fortune is far larger than the median because of a few very rich people.