Track 3 · Visualising and Exploring Data · Lesson 3 of 11
Histograms
Build and read a histogram, describe the shape of a distribution, and judge how the choice of bins changes what the chart shows.
Before a company changes its shift times it wants to know how long commutes really are: are most people close to the average, or is there a long tail of very long journeys? A histogram answers that in one glance — provided its bins are chosen sensibly.
A histogram shows the distribution of one numeric variable. Divide the number line into adjacent intervals called bins, count how many observations fall in each, and draw a bar over each bin whose height is that count. Unlike a bar chart of categories, the bars touch: the horizontal axis is a continuous scale, and the bins tile it with no gaps.
Two conventions matter when you read one exactly:
- Bins here are left-closed: the bin from 20 to 24 contains 20 but not 24 (24 belongs to the next bin). The last bin also includes the maximum.
- All bins have the same width unless stated otherwise, so bar heights can be compared directly.
Included with a Formula Quest membership
It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Build a histogram with left-closed, equal-width bins and read counts from it exactly
- Describe a distribution by its shape, centre, spread and unusual values
- Compute a Freedman–Diaconis bin width and explain how bin width changes the picture
- Use density (count ÷ n ÷ width) when bins have unequal widths