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How to Make a Histogram with Class Boundaries?

Published in Histogram Creation 4 mins read

Creating a histogram with class boundaries involves several key steps to accurately visualize the distribution of your data. Here's a breakdown:

Understanding Class Boundaries

Class boundaries are the precise values that separate one class (or bin) in a histogram from the next. They eliminate any gaps between the bars, making the histogram a contiguous visual representation of the data.

Steps to Create a Histogram with Class Boundaries

  1. Determine the Data Range: Find the minimum and maximum values in your dataset. This defines the overall range your histogram will cover.

  2. Decide on the Number of Classes: Determine how many bars (or classes) your histogram will have. This choice can impact the histogram's clarity; too few bars may hide detail, while too many can make it difficult to see the pattern. A common rule of thumb is the square root of the number of data points, but it depends on the specific dataset.

  3. Calculate Class Width: Once you know the number of classes, the width of each class is calculated by dividing the range of the data (maximum value minus minimum value) by the number of classes.

    • Formula: Class width = (Maximum Value - Minimum Value) / Number of Classes

  4. Establish Class Boundaries:

    • Start with the lower boundary of the first class, usually slightly below the minimum value of your data.
    • Add the class width to the lower boundary to get the upper boundary of the first class and the lower boundary of the second class.
    • Continue adding the class width to determine all the upper and lower boundaries for all classes.

  5. Tally Frequencies: Count how many data points fall within each class, being careful to use the class boundaries to place data correctly.

  6. Draw the Histogram: As explained in the reference video ([Part of a video titled What Is And How To Construct Draw Make A Histogram ... - YouTube]()), you’ll now draw bars for each class, whose height corresponds to the frequency within that class. The bars should be contiguous with no gaps between them because you are using class boundaries.

  • Draw the lines to mark the edges of each bar and then fill in the bar up to the level of the frequency.

Example

Let’s say you want to make a histogram from the following data:
12, 15, 18, 20, 22, 23, 25, 26, 28, 30, 33, 35, 37, 39, 40, 42, 45

  1. Data Range: The minimum value is 12, and the maximum value is 45.

  2. Number of Classes: Let's choose 5 classes.

  3. Class Width: (45 - 12) / 5 = 6.6, so we can round this to 7 for simpler calculations.

  4. Class Boundaries:

    • Class 1: 11.5 - 18.5
    • Class 2: 18.5 - 25.5
    • Class 3: 25.5 - 32.5
    • Class 4: 32.5 - 39.5
    • Class 5: 39.5 - 46.5

  5. Frequencies:

    • Class 1 (11.5 - 18.5): 3
    • Class 2 (18.5 - 25.5): 4
    • Class 3 (25.5 - 32.5): 3
    • Class 4 (32.5 - 39.5): 4
    • Class 5 (39.5 - 46.5): 3

  6. Now, use these frequencies to draw the bars for each class. The example in the reference video shows how to draw the lines and fill in the bars according to the corresponding frequency.

Key Points

  • Class boundaries should be continuous with no gaps between the bars.
  • Ensure accurate tallying of frequencies for each class.
  • Choose the number of classes wisely, as it can affect the visualization of the data.
  • The reference video ([Part of a video titled What Is And How To Construct Draw Make A Histogram ... - YouTube]()) gives a good demonstration of the drawing of the histogram and emphasizes filling in the bars.

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