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How to Make a Frequency Polygon?

Published in Data Visualization 2 mins read

To create a frequency polygon, follow these steps to visually represent the distribution of your data.

Steps to Construct a Frequency Polygon

  1. Determine Class Intervals (Bins): Decide on the range and number of class intervals into which you'll group your data. Choose intervals of equal size for consistency.

  2. Calculate Midpoints: Find the midpoint of each class interval. The midpoint is calculated as (Lower Class Limit + Upper Class Limit) / 2. These midpoints will be plotted on the x-axis.

  3. Label the Axes:

    • X-axis: Label the horizontal axis with the midpoints of each class interval.
    • Y-axis: Label the vertical axis with the frequency (count) of observations falling within each respective class interval.

  4. Plot the Points: For each class interval, plot a point above the midpoint on the x-axis at a height corresponding to the frequency on the y-axis.

  5. Connect the Points: Connect the plotted points with straight lines.

  6. Close the Polygon: Extend the polygon to the x-axis at both ends. This is done by adding an imaginary class interval below the lowest interval and above the highest interval, each with a frequency of zero. This ensures the polygon "closes" on the x-axis.

Example

Let's say you have the following data representing test scores:

Class Interval Frequency Midpoint
60-69 5 64.5
70-79 10 74.5
80-89 15 84.5
90-99 8 94.5

  1. Class Intervals: As shown above.

  2. Midpoints: Calculated as shown above (e.g., for 60-69: (60+69)/2 = 64.5).

  3. Axes: X-axis labeled with midpoints (64.5, 74.5, 84.5, 94.5), Y-axis labeled with frequencies (0 to 15+).

  4. Plot Points: Plot (64.5, 5), (74.5, 10), (84.5, 15), (94.5, 8).

  5. Connect Points: Draw straight lines connecting the points.

  6. Close Polygon: Add imaginary class intervals: 50-59 (midpoint 54.5, frequency 0) and 100-109 (midpoint 104.5, frequency 0). Plot (54.5, 0) and (104.5, 0), and connect these to the endpoints of the existing lines.

Key Considerations:

  • Frequency polygons are excellent for comparing multiple distributions on the same graph. You can plot multiple frequency polygons on the same axes, allowing for a direct visual comparison of the shape and spread of different datasets.
  • The area under a frequency polygon approximates the total number of observations.

By following these steps, you can effectively create a frequency polygon to represent your data visually.

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