Histogram and Frequency Polygon

A continuous grouped frequency distribution can be represented graphically by a histogram. A histogram is a vertical bar graph with no space between the bars.

Histogram

  1. The classes of the grouped data are taken along the horizontal axis.
  2. The respective class frequencies are taken on the vertical axis, using a suitable scale on each axis.
  3. For each class, a rectangle is constructed with base as the width of the class and height determined from the class frequencies. The areas of rectangles are proportional to the frequencies of their respective classes.

Example

Frequency Polygon

Let B, C, D, E, F and G be the mid points of the tops of the adjacent rectangles. Join B to C, C to D, D to E, E to F and F to G by means of line segments (dotted).

To complete the polygon, join B to A (the mid point of class 10-20) and join G to H (the mid point of the class 80-90).

Thus, ABCDEFGH is the frequency polygon representing the data.

A frequency polygon is obtained by first joining the mid points of the tops of the adjacent rectangles in the histogram and then joining the mid point of first rectangle to the mid point of the class preceding the lowest class and the the last mid point to the mid point of the class succeeding the highest class.

A frequency polygon can also be drawn independently without drawing a histogram by using the class marks of the classes and respective frequencies of the classes.