Frequency distribution is a method used to organize raw data in a structured manner by grouping the data into classes or intervals and showing the number of observations (frequency) in each class. It provides a clear and concise representation of the distribution of data across different categories or intervals, making it easier to analyze and interpret the data.

Components of Frequency Distribution:

1. Class Intervals (or Classes):
   • Ranges or intervals into which the data is grouped.
   • The width of each class interval should be consistent and not overlap.
   • Examples: 0-10, 11-20, 21-30, …
2. Frequency:
   • The number of observations or data points falling into each class interval.
   • Represented by 
     $$f 

     fi​ for individual class frequencies.

3. Cumulative Frequency:
   • The running total of frequencies as you move down the frequency distribution table.
   • Helps in understanding the total number of observations up to a certain class interval.

Steps to Construct a Frequency Distribution:

1. Determine the Range and Number of Classes:
   • Calculate the range (difference between the maximum and minimum values) of the data.
   • Decide on the number of classes based on the range and the desired level of detail.
2. Calculate the Class Width:
   • Determine the width of each class interval by dividing the range by the number of classes and rounding up to a convenient number.
3. Set Up the Frequency Distribution Table:
   • Create columns for class intervals, frequencies, and cumulative frequencies (optional).
4. Group the Data into Classes:
   • Sort the data in ascending order.
   • Assign each data point to the appropriate class interval based on its value.
5. Count the Frequencies:
   • Count the number of data points falling into each class interval.
6. Calculate Cumulative Frequencies:
   • Calculate the running total of frequencies.

Example of Frequency Distribution:

Suppose you have the following scores of students in a class test:

$68,72,75,80,85,88,90,92,95,98$

68,72,75,80,85,88,90,92,95,98

To construct a frequency distribution table:

1. Determine the Range and Number of Classes:
   • Range = 98 – 68 = 30
   • Number of classes = 5 (for simplicity)
2. Calculate the Class Width:
   • Class width =
     
     $\frac{30}{5}$

      

      

     530​ = 6 (round up)

3. Set Up the Frequency Distribution Table:

This frequency distribution table provides a clear overview of how the scores are distributed across different intervals, making it easier to analyze and interpret the data.