# Frequency Polygons

A frequency polygon is almost identical to a histogram, which is used to compare sets of data or to display a cumulative frequency distribution. It uses a line graph to represent quantitative data.

Statistics deals with the collection of data and information for a particular purpose. The tabulation of each run for each ball in cricket gives the statistics of the game. Tables, graphs, pie-charts, bar graphs, histograms, polygons etc. are used to represent statistical data pictorially.

In the upcoming discussion let us discuss how to represent a frequency polygons. These are visually substantial method of representing quantitative data and its frequencies.

To draw frequency polygons, we begin with, drawing histograms and follow the following steps:

**Step 1-**Choose the class interval and mark the values on the horizontal axes**Step 2-**Mark the mid value of each interval on the horizontal axes.**Step 3-**Mark the frequency of the class on the vertical axes.**Step 4-**Corresponding to the frequency of each class interval, mark a point at the height in the middle of the class interval**Step 5-**Connect these points using the line segment.**Step 6-**The obtained representation is a frequency polygon.

**Example 1: In a batch of 400 students, the height of students is given in the following table. Represent it through a frequency polygon.**

**Solution:** Following steps are to be followed to construct a histogram from the given data:

- The heights are represented on the horizontal axes on a suitable scale as shown.
- The number of students is represented on the vertical axes on a suitable scale as shown.
- Now rectangular bars of widths equal to the class- size and the length of the bars corresponding to a frequency of the class interval is drawn.

ABCDEF represents the given data graphically in form of frequency polygon as:

Frequency polygons can also be drawn independently without drawing histograms. For this, the midpoints of the class intervals known as class marks are used to plot the points.