Two histogram bars can have the same height without representing the same proportion of observations. When the vertical axis shows density, the width of each interval matters too.
Suppose an illustrative bar has width 2 and height 0.1. Its area is 0.2. Another bar with width 1 and height 0.2 has the same area. Under probability-density normalisation, equal areas represent equal proportions, despite the different heights.
The NIST discussion of histograms distinguishes normalisations, including one in which total bar area is one. Check the axis label and the software’s settings before applying this interpretation.
A useful margin calculation
Choose one interval and calculate height multiplied by width. Compare that with the fraction of observations assigned to the interval. Use a small example whose bins you can count manually before moving to a large dataset.
Do not add density heights as if they were percentages. That shortcut ignores interval width and can produce a meaningless total.
For a published chart, describe both the measured variable and the vertical-axis quantity. “Density” may be familiar to the analyst, but the caption should help a reader understand why a taller bar is not automatically a larger share when widths differ.