A summary statistic like the mean or the median frequently hides relevant information. That's why in both The Functional Art and The Truthful Art I wrote —borrowing from Nigel Holmes— that data visualization and infographics shouldn't simplify information; they are instruments for clarification. Clarifying a story very often involves increasing, not reducing, the amount of data shown to readers.
Take this story about crime statistics, published today by The New York Times. If you report just the national homicide rate, you're doing your audience a disservice, as that single data point is highly skewed by a few outliers, specific neighborhoods in certain cities. As this good article about amalgamation paradoxes explains, things that look one way at the group level (“positive correlation!”) may look very different when analyzed at an individual level (“negative correlation!”). Here's the chart the authors use:
