Histograms
When numerical data are too many or too spread out to draw one by one, how can bars still show where they crowd together?
Where you are 4 inside
What this area is about
A histogram cuts the number line into bins of equal width that run end to end, then stands a bar on each bin as tall as the number of values in it. It is for numerical data, and it helps most when the values are many or rarely repeat, so a dot plot would show no clusters. The price is that a bar says how many values fall in a bin, never which ones.
How these fit together
Reading and making. Reading a histogram gets counts and totals from the bars, with a fixed rule for a value on an edge. Making a histogram goes the other way, from a list to a frequency table to bars, and asks how wide the bins should be.
Shares instead of counts. Relative frequency histograms give each bar the height \displaystyle \frac{f}{n}, a bin’s count over the total, so groups of different sizes can be compared; the heights add to 1.
Running totals. Cumulative frequency graphs and percentiles add the bars from the left and draw a rising line, so the share of values below any point is read off one curve.
A path through it
Read a histogram first (making one reuses its edge rule), then make one. Relative frequency builds on making, and cumulative frequency on relative frequency.
Finish here and you can describe the shape of a distribution, and the same bar picture leads on to probability distribution tables and density curves.