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Class interval can be divided into two categories:
Continuous series:
When there is no break between two classes given in numerical order, it is called a continuous series.
Example:
Class \(1\): \(0\) - \(10\)
Class \(2\): \(10\) - \(20\)
Class \(3\): \(20\) - \(30\)
In this example, there is no gap between classes \(1\) and \(2\); similarly, there is no gap between classes \(2\) and \(3\).
Discontinuous series:
When there is a break or gap between two classes given in numerical order, it is called a discontinuous series.
Example:
Class \(1\): \(0\) - \(10\)
Class \(2\): \(11\) - \(20\)
Class \(3\): \(21\) - \(30\)
In this example, there is a gap of \(1\) unit between classes \(1\) and \(2\); similarly, there is a gap of \(1\) unit between classes \(2\) and \(3\).
Can a discontinuous series be converted into a continuous series?
Yes, a discontinuous series can be converted into a continuous series in a few steps.
Let us look at it in detail using the following example.
Class \(1\): \(5\) - \(20\)
Class \(2\): \(25\) - \(40\)
Class \(3\): \(45\) - \(60\)
Step \(1\): Consider the gap between the classes \(1\) and \(2\).
Class \(1\) ends with \(20\), and class \(2\) begins with \(25\).
Therefore, the gap between classes \(1\) and \(2\):
\(25 - 20 = 5\)
Gap between class \(1\) and class \(2 = 5\)
Step \(2\): Convert class \(1\) into a continuous series.
Class \(1\): \(5\) - \(20\)
Gap between class \(1\) and class \(2 = 5\)
\(\text{Lower boundary} = \text{Lower limit} - \text{Half of the gap}\)
\(= 5 - \frac{1}{2}(5)\)
\(= 5 - 2.5\)
\(= 2.5\)
Lower limit of class \(1 = 2.5\)
\(\text{Upper boundary} = \text{Upper limit} + \text{Half of the gap}\)
\(= 20 + \frac{1}{2}(20)\)
\(= 20 + 2.5\)
\(= 22.5\)
Upper limit of class \(1 = 22.5\)
Now, the updated limit of class \(1\) is \(2.5\) - \(22.5\).
Step \(3\): Apply steps \(1\) and \(2\) to all the other classes available in a series and make the required conversion.
Now, the continuous series converted from the discontinuous series will look like this.
Class \(1\): \(2.5\) - \(22.5\)
Class \(2\): \(22.5\) - \(42.5\)
Class \(3\): \(42.5\) - \(62.5\)
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