Dot Plots and Box Plots

A dot plot puts one dot above the number line for every value in a data set, so you can see the actual shape of the data: where it clusters, where it spreads, and any gaps or outliers. A box plot trades that detail for a cleaner summary. It plots five numbers — the minimum, the lower quartile (Q1), the median, the upper quartile (Q3), and the maximum — and draws a box from Q1 to Q3 with whiskers stretching to the extremes. You lose the individual points, but you gain a quick read on center and spread, which is often all you need to compare groups.

The five numbers cut the ordered data into four pieces, each holding about one quarter of the values. That is the whole trick: the median splits the data in half, then the lower and upper quartiles split each half again. So the stretch from the minimum to Q1 holds about a quarter of the data, Q1 to the median another quarter, the median to Q3 another quarter, and Q3 to the maximum holds the last quarter. The box itself, from Q1 to Q3, always holds about half the data — no matter how wide or narrow it looks. Width on a box plot measures spread along the scale, not population, so a wide box can hold the same half of the data as a narrow one; it's just more spread out.

This is why box plots pair naturally with the idea of distribution shape and spread used elsewhere in data analysis. The interquartile range, Q3 minus Q1, measures the spread of that middle half and is the box plot's version of a typical spread, resistant to outliers the way range is not.