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How to Draw a Histogram From a Frequency Table?

Published in Data Visualization 3 mins read

Drawing a histogram from a frequency table involves several key steps focused on accurately representing the data's distribution. Here's how you can do it:

Understanding Frequency Tables and Histograms

Before diving into the process, it's crucial to understand what these tools represent. A frequency table organizes raw data by listing different intervals (or classes) and the number of data points falling into each interval (the frequency). A histogram, on the other hand, is a visual representation of this distribution, where the area of each bar corresponds to the frequency of each interval.

Steps to Draw a Histogram

Here’s a detailed breakdown of the process, incorporating the information from our references:

  1. Calculate Frequency Density:

    • The key to creating an accurate histogram lies in the concept of frequency density.
    • Frequency density is calculated by dividing the frequency of a class interval by the width of that interval.
    • Formula: Frequency Density = Frequency / Class Width.
    • For example, if an interval is 10-20 with a frequency of 25, and another interval is 20-25 with a frequency of 10.
    • The first frequency density would be 25 / (20 - 10) = 25 / 10 = 2.5
    • The second frequency density would be 10 / (25-20) = 10 / 5 = 2
  2. Create Axes:

    • Determine appropriate axes for your histogram.
    • The horizontal axis (x-axis) will represent your class intervals (e.g., ranges of values).
    • The vertical axis (y-axis) will represent the frequency density. It is very important to use frequency density, not frequency.
    • Label your axes clearly to make your histogram understandable.
  3. Draw the Bars:

    • For each class interval, draw a bar.
    • The width of the bar corresponds to the class interval itself.
    • The height of the bar is determined by the frequency density you calculated for that interval.
    • Bars in a histogram touch each other, emphasizing that the data is continuous, although data in frequency tables is sometimes discrete.

Example Table and Drawing

Let's imagine the following frequency table to solidify the explanation:

Class Interval Frequency Class Width Frequency Density
0 - 10 5 10 0.5
10 - 20 15 10 1.5
20 - 40 20 20 1
40 - 50 10 10 1
  • Step 1: Frequency densities were calculated as shown in the table.
  • Step 2: The horizontal axis would range from 0 to 50, and the vertical axis, based on the highest frequency density, would likely go up to about 2.
  • Step 3: You would then draw bars such that:
    • The bar from 0 to 10 would have a height of 0.5
    • The bar from 10 to 20 would have a height of 1.5.
    • The bar from 20 to 40 would have a height of 1.
    • The bar from 40 to 50 would have a height of 1.

Important Considerations

  • Unequal Class Widths: This is where frequency density becomes essential. When your class intervals have different widths, using only the frequency can distort the visual representation, making some intervals seem more prominent than they are. Using the density corrects this.
  • Starting and Ending Points: Make sure your x-axis correctly reflects the starting and ending values of your intervals.
  • Software: There are numerous programs like Excel or Python libraries (like Matplotlib) that can automate this process, which is very helpful for large datasets.

By following these steps, you can accurately create a histogram from any frequency table, which provides valuable insights into the data's distribution.