Class Interval

In statistics, class intervals are used to group data into specific ranges. This makes it easier to organize and analyze data efficiently. It is especially useful when we deal with continuous data, where the individual data values vary continuously over a range.

By grouping data into intervals it makes it easier to identify patterns and trends. Class intervals are defined with two values which are lower limits the smallest values in a class interval and
upper limit the largest value in a class interval.
 

We know that data is categorized into two types: Grouped and ungrouped. Here is the formula to calculate class intervals:

Class Interval = Upper Limit - Lower Limit

Class width = (Range of data) / (Number of class intervals)

In class, width: Range of data = Maximum value - minimum value

Step 1: First, we find the minimum and maximum values in the dataset.


Step 2: Next, we calculate the range.


Step 3: Choose the number of class intervals


Step 4: Calculate the class width using the formula


Step 5: Create the intervals.
 

To find class intervals of datasets accurately, we follow these steps:

Step 1: To find the range, subtract the minimum value of the dataset from the maximum value. 

Step 2: Next, choose the amount of intervals based on the size of the dataset. 

Step 3: Calculate the class width. We do this by dividing the range by the number of intervals you have decided. 

Step 4: Organize the data into suitable intervals.

Class intervals are categorized into different types based on how they are structured and what kind of data we want to represent:

• Exclusive Class Interval
  
   
• Inclusive Class Interval
   

 Exclusive class intervals are when the lower bound or the minimum value is included in the interval and the upper bound or maximum value is excluded. This means that any data point equal to the upper bound is assigned to the previous interval. For example, in the interval (10, 20), include from 10 to 19.999, but not 20.

As you can see in this table, in an exclusive class interval, the next class interval’s lower limit is equal to the upper limit of the previous interval.

 In inclusive class intervals, both the lower limit and upper limits are included within the interval. We use inclusive class intervals when we want to ensure that all the data values in the data set are equal to the limits that are part of that interval.

In this case, both lower and upper limits are included in the interval and the upper limit of one class interval is different from the lower limit of the next class interval.
 

Class intervals can be represented graphically using graphs such as histograms or frequency polygons. Class intervals show how data is distributed across different ranges. These graphs help in visualizing trends and frequencies in the dataset.

To represent a class interval graphically:

Step 1: Prepare a frequency table by organizing the data into class intervals, and then we count the number of values in each interval.

Step 2: Label the axes, the x-axis will represent the class intervals and the y-axis will represent the frequency. 

Step 3: Plot the data by taking the frequency for each interval which is marked as a bar, point, or curve depending on the graph used. In most cases, intervals are continuous, meaning the bars or points are connected without any gaps.

This is a general approach that gets applied to different types of graphs like histograms or frequency polygons, etc.
 

Class intervals are widely used in various fields in the real world. Here are a few real-world applications of class intervals:

 

• Education: Schools and colleges use class intervals to group students' scores into ranges. This helps teachers analyze the students’ performance.
  
   
• Market research: Class intervals are used in market research to categorize survey responses or customer feedback into different ranges.
  
   
• Financial Analysis: In finance, we use class intervals to group income levels or investment returns into ranges to identify the trends or plan budgeting.