Histograms

A list of numbers is hard to see. A histogram turns it into a picture of shape. The recipe is three steps:

Bin the range of the data into equal-width intervals.
Count how many values fall in each bin.
Draw a bar over each bin whose height is that count.

Tall bars mark the values that occur often; the overall silhouette reveals where the data pile up and how they tail off. Note the bars sit flush against each other — the data are continuous, so there are no gaps between bins (this is what separates a histogram from a bar chart).

The bin width changes the picture

Here is one fixed data set of 30 values, drawn twice. The first histogram uses a narrow bin width of 2; the second uses a wide bin width of 5 — exactly the same numbers, only the binning differs.

The narrow bins reveal the real shape: a hump around 5–7 with a tail trailing off to the right. The wide bins flatten that story into three blunt bars — the peak and the tail are smeared together. Too wide hides the detail; too narrow (a width of, say, 0.5) would splinter the data into a spiky, near-empty mess. Choosing a sensible bin width is half the craft of a good histogram.

A histogram bins the range, counts per bin, and draws a bar whose height is the count.
The bars touch (no gaps) because the underlying data are continuous.
The bin width is a choice: too wide hides detail, too narrow makes the picture spiky and noisy.
The silhouette shows where the data pile up and how the tails stretch.