Graphic Representation of Data — Histogram and Frequency Polygon

Diagrams such as bar charts and pie charts suit discrete categories; when the data is instead a continuous frequency distribution (values grouped into class intervals, such as marks or wages grouped into class-widths of 10), it is presented as a graph, plotted on two perpendicular axes.

A histogram is a set of adjoining rectangles drawn over the class intervals of a continuous frequency distribution: the class intervals are marked along the X-axis with no gaps between consecutive bars (since the classes themselves are continuous), and the frequency of each class is shown as the height of the rectangle above it. Where class intervals are of unequal width, the height must instead be adjusted to frequency density (frequency divided by class width), so that the area of each rectangle, not merely its height, stays proportional to its frequency. Where the given classes are in inclusive form (e.g., 0–9, 10–19), they must first be converted to continuous, exclusive form (e.g., −0.5–9.5, 9.5–19.5) before the histogram is drawn, since a histogram requires the boundaries of successive classes to meet exactly.

A frequency polygon presents the same information as a many-sided line figure instead of solid blocks. It can be obtained in either of two equivalent ways: (i) by joining the midpoints of the tops of the histogram's bars with straight lines, or (ii) independently, by plotting each class's frequency against its own mid-value and joining the plotted points with straight lines. In either case, the figure is closed at both ends by joining it to the base line (zero frequency) one class-width beyond the first and last classes, so the enclosed area represents the whole distribution.

| Basis | Histogram | Frequency Polygon |

|---|---|---| …