Class interval is a term that is used to denote the numerical width of a class in a frequency distribution. In a grouped frequency distribution, data is arranged in the form of a class. The difference between the upper-class limit and the lower limit gives the class interval.
In statistics, there are two types of class intervals, namely exclusive and inclusive class intervals. Based on these, a frequency distribution table can be constructed. In this article, we will learn more about a class interval, its types, formula, graph, and see some examples.
|1.||What is Class Interval in Statistics?|
|2.||Class Interval Formula|
|3.||Inclusive Class Interval|
|4.||Exclusive Class Interval|
|5.||Class Interval Histogram|
|6.||FAQs on Class Interval|
What is Class Interval in Statistics?
A class interval is used in a frequency distribution table to organize the data obtained from an experiment systematically. The classes in a frequency distribution are usually mutually exclusive. A histogram can be easily constructed by using class intervals.
Definition of Class Interval
A class interval can be defined as the difference between the upper and lower class limit of a frequency distribution table. In other words, it is the width of each class. A grouped frequency distribution can be sorted either on the basis of exclusive or inclusive class intervals.
Class Interval Example
Suppose there is a class given by 11 - 21. 11 will be known as the lower class limit while 21 is the upper limit. The class interval is given by 21 - 11 = 10.
Class Interval Formula
To determine the class interval, the lower limit of the class is subtracted from the upper limit. The class interval formula is given as follows:
Class interval = Upper Limit - Lower Limit.
Inclusive Class Interval
An inclusive class interval is created using the inclusive method of sorting data into a frequency distribution table. In such a method, the lower limit of a class does not get repeated in the upper limit of the preceding class. When a frequency distribution is analyzed the inclusive class interval has to be converted to an exclusive class interval. This can be done by subtracting 0.5 from the lower class limit and adding 0.5 to the upper class limit. An example of an inclusive class interval is given below:
|10 - 19||9.5 - 19.5||2|
|20 - 29||19.5 - 29.5||5|
|30 - 39||29.5 - 39.5||1|
Exclusive Class Interval
In an exclusive class interval, the upper limit of one class is the same as the lower limit of the succeeding class. This method of sorting data ensures continuity between two consecutive classes. The value of the mean, median, and mode will be the same irrespective of whether the frequency distribution table has an inclusive or exclusive class interval. Given below is an example of an exclusive class interval.
|10 - 20||2|
|20 - 30||5|
|30 - 40||1|
Class Interval Histogram
A histogram is used for visually representing a continuous frequency distribution table. An exclusive class interval can be directly represented on the histogram. However, an inclusive class interval needs to be first converted to an exclusive class interval before graphically representing it. The x-axis represents the class interval and the y axis represents the corresponding frequency.
Suppose a frequency distribution table is given as follows:
|0 - 10||8|
|10 - 20||12|
|20 - 30||16|
|30 - 40||14|
|40 - 50||10|
|50 - 60||5|
The class interval histogram is given below:
Important Notes on Class Interval
- A class interval can be defined as the width of the class.
- The class interval formula is given as upper limit - lower limit.
- In an exclusive class interval, the upper limit of one class is the same as the lower limit of the next class.
- In an inclusive class interval, the upper class limit of one class does not get repeated in the lower limit of the succeeding class.
Examples on Class Interval
Example 1: What is the class interval of the following frequency distribution table?
Class Frequency 15 - 22 4 22 - 29 8 29 - 36 5 36 - 43 1
Solution: The is an exclusive class interval. The class interval formula is upper limit - lower limit.
Class Class Interval 15 - 22 22 - 15 = 7 22 - 29 29 - 22 = 7 29 - 36 36 - 29 = 7 36 - 43 43 - 36 = 7
Example 2: What is the class interval for the given classes?
Class 12 - 15 16 - 19 20 - 23 24 - 27 28 - 31 32 - 35
Solution: This is an inclusive class interval. Thus, the class needs to be converted to an exclusive class interval.
Class Adjusted Class Class interval 12 - 15 11.5 - 15.5 4 16 - 19 15.5 - 19.5 4 20 - 23 19.5 - 23.5 4 24 - 27 23.5 - 27.5 4 28 - 31 27.5 - 31.5 4 32 - 35 31.5 - 35.5 4
Example 3: Draw a histogram for the following frequency distribution and determine the class interval.
Class Frequency 16 - 20 10 21 - 25 15 26 - 30 25 31 - 35 30
Solution: Converting the class to an exclusive class interval.
Class Adjusted class Class Interval Frequency 16 - 20 15.5 - 20.5 5 10 21 - 25 20.5 - 25.5 5 15 26 - 30 25.5 - 30.5 5 25 31 - 35 30.5 - 31.5 5 30
FAQs on Class Interval
What is a Class Interval?
A class interval can be defined as the size of a class in a grouped frequency distribution. It is the difference between the upper class limit and the lower class limit.
What is the Formula for Class Interval?
The formula to calculate the class interval is given by subtracting the lower class limit from the upper class limit.
Class interval = Upper limit - Lower limit.
What are the Types of Class Interval in Statistics?
There are two types of class intervals in statistics. These are given as follows:
- Inclusive class interval
- Exclusive class interval
What is an Inclusive Class Interval?
An inclusive class interval is one in which the lower class limit of a class is not repeated in the upper class limit of the preceding class. Example, 0 - 5, 6 - 11, 12 - 17.
What is an Exclusive Class Interval?
In an exclusive class, the lower limit of one class is the same as the upper limit of the preceding class. Example, 0 - 5, 5 - 10, 10 - 15.
How to Convert an Inclusive Class Interval to an Exclusive Interval?
An inclusive class interval can be converted to an exclusive interval by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit.
Can a Histogram Be Plotted for an inclusive Class Interval?
No, a histogram cannot be plotted for an inclusive class interval. This is because it will result in a gap between the bars. Thus, such a class interval has to be converted to an exclusive interval before a histogram can be drawn.