How to Make a Frequency Distribution?

Making a frequency distribution involves organizing raw data into a meaningful summary of how often different values occur. Here's a step-by-step guide:

1. Calculate the Range: Determine the difference between the highest and lowest values in your dataset. This tells you the spread of your data.

   • Example: If your highest value is 100 and your lowest is 20, the range is 100 - 20 = 80.

2. Determine the Number of Classes (Groups): Decide how many groups (or intervals) you want to divide your data into. There's no hard and fast rule, but 5-20 classes are generally recommended. Consider the size and nature of your data. More data often allows for more classes.

3. Calculate the Class Width: Divide the range by the desired number of classes. Round the result up to the nearest whole number (or a suitable level of precision) to ensure all data is included.

   • Formula: Class Width = Range / Number of Classes
   • Example: If your range is 80 and you want 10 classes, the class width would be 80 / 10 = 8. Rounding up to 8 keeps it simple.

4. Create the Classes: Define the lower and upper limits for each class. Start with the lowest value in your dataset as the lower limit of the first class. Add the class width to this lower limit to find the upper limit of the first class. The lower limit of the next class will be one unit higher than the upper limit of the previous class (assuming you're working with whole numbers; adjust accordingly for decimals).

   • Example:
     • Class 1: 20-27 (Lowest value is 20, width is 8, so 20 + 8 - 1 = 27)
     • Class 2: 28-35
     • Class 3: 36-43
     • And so on...

5. Tally the Frequencies: Go through your data and count how many values fall within each class. This count is the frequency for that class.

6. Create the Frequency Distribution Table: Organize your classes and their corresponding frequencies into a table. You can optionally include other columns, such as relative frequency (frequency divided by the total number of data points), cumulative frequency (the sum of frequencies up to that class), and class midpoints (the average of the lower and upper class limits).

   • Example Table:

     Class	Frequency	Relative Frequency	Cumulative Frequency
     20-27	5	0.10	5
     28-35	8	0.16	13
     36-43	12	0.24	25
     44-51	10	0.20	35
     ...	...	...	...

In summary, creating a frequency distribution involves determining the range, deciding on the number and width of classes, assigning data points to those classes, and organizing the results into a table for easy interpretation.