Graphic Presentation — Histogram

A graph presents a continuous frequency distribution on a coordinate system (an x-axis and a y-axis), unlike a diagram, which represents discrete items as bars or sectors.

A histogram represents a continuous frequency distribution as a set of adjoining rectangles, one per class interval, drawn on the class boundaries (never the class limits — an inclusive-method table must first be converted to exclusive boundaries, as shown in the frequency-distribution section above). Because the rectangles touch each other with no gap, a histogram visually communicates that the underlying variable is continuous.

When all class widths are equal, the height of each rectangle is simply the class frequency itself.

When class widths are unequal, using the raw frequency as the height would be misleading — a wider class would look 'taller' just because it covers more ground. The correct height is the frequency density: $\text{height} = \dfrac{\text{class frequency}}{\text{class width}}$. This way, the area of each rectangle (height × width) stays proportional to its frequency, which is the real statistical meaning of a histogram — area represents frequency, not height alone.

A histogram must never be confused with a bar diagram: a bar diagram's bars are separated by gaps and represent discrete categories; a histogram's rectangles touch and represent a continuous variable divided into class intervals. …