We can find the class interval using the formula,

Class Interval = Upper Limit of Class – Lower Limit of Class.

We organize data in the form of class intervals in order to present the data in a compact and concise form. The class interval is nothing but the length of the class in a grouped frequency distribution.

**How to Find Class Intervals?**

- Identify the classes of the given distribution.
- Write down the upper and lower limits of each class.
- Subtract the lower limit from the upper in order to obtain the width for that class.

**Class Interval Formula**

The class interval can be calculated using the formula,

Class Interval = U – L.

- U is the upper class limit.
- L is the lower class limit of the given class interval.

**Example 1:**

Consider the following grouped frequency distribution table:

Class | Frequencies |

0-10 | 7 |

10-20 | 3 |

20-30 | 15 |

30-40 | 5 |

40-50 | 7 |

50-60 | 9 |

60-70 | 8 |

The size of the class 30-40 is the difference between 30 and 40 which is 10. Here we see that the size of each class is 10. Hence class width for each class in this example is 10.

Class | Frequencies | Lower Limit (L) | Upper Limit (U) | Class Interval= U-L |

0-10 | 7 | 0 | 10 | 10-0= 10 |

10-20 | 3 | 10 | 20 | 20-10= 10 |

20-30 | 15 | 20 | 30 | 30-20= 10 |

30-40 | 5 | 30 | 40 | 40-30= 10 |

40-50 | 7 | 40 | 50 | 50-40= 10 |

50-60 | 9 | 50 | 60 | 60-50= 10 |

60-70 | 8 | 60 | 70 | 70-60= 10 |

In the above example, the class widths for each class were equal. It can also be the case that we have unequal class lengths for each class.

**Example 2:**

Consider the following frequency distribution table:

Class Intervals | Frequencies |

5-10 | 7 |

10-12 | 3 |

12-15 | 15 |

15-25 | 5 |

25-45 | 7 |

45-50 | 9 |

The class width of the class 45-50 is 5 whereas the class width of the class 25-45 is 20.

Therefore, the class widths are unequal in the above example. We compute all of the class widths are follows:

Class | Frequency | Lower Limit (L) | Upper Limit (U) | Class Interval |

5-10 | 7 | 5 | 10 | U-L = 10-5 =5 |

10-12 | 3 | 10 | 12 | U-L = 12-10 = 2 |

12-15 | 15 | 12 | 15 | U-L = 15-12 = 3 |

15-25 | 5 | 15 | 25 | U-L = 25 – 15 = 10 |

25-45 | 7 | 25 | 45 | U-L = 45-25 = 20 |

45-50 | 9 | 45 | 50 | U-L = 50 – 45 =5 |

**Types of Class Intervals**

When dealing with a large set of data values it is convenient to divide the data into intervals of equal length called class intervals.

The class intervals formed are of two types – Inclusive Class Intervals and Exclusive Class Intervals.

**Inclusive Class Intervals**

**In an inclusive** **classification, the upper limit of a class is not equal to the lower limit of the next class.**

By the intervals being inclusive we mean that both the upper and lower limits of the interval are included in the interval.

So in the example below, we have a frequency of 3 for the interval 30-39. This means that there a three data points whose value lies between 30 and 39 including 30 and 39 themselves.

For instance, the three values could be 30, 34, and 39.

**Exclusive Class Intervals**

**In an exclusive classification, the upper limit of a class is equal to the lower limit of the next class.**

Generally speaking, in exclusive class intervals upper limit of the interval is not considered to be a part of the values covered by that interval.

For example, in the table below the interval, 15-20 has a frequency of 5. This means that there are 5 data points taking values between 15 and 20 where 15 is allowed but 20 is excluded.

For instance, the 5 data points 15, 16, 17, 17, and 18 would be considered to belong to this interval.

On the other hand, the data values 15, 16, 17, 18, and 20 would not be considered to be part of this interval since 20 is excluded from this interval. The value 20 belongs to the next class interval which is 20-25.