The class limit corresponds to a class interval and the class limits are defined as the minimum value and the maximum value of the class interval may be contained. The maximum value in the class is known as the Upper-class limit whereas the minimum value in the class is known as the Lower class limit. The Lower Class Limit is represented as LCL and the Upper-Class Limit is represented as UCL. Class limits have two series (or) form one is exclusive series (or) form and another one is inclusive series (or) form.

The Upper-Class Limit of a class is the largest data value that will go into the class and the lower class limit of a class is the smallest data value that can go into the class. Class limits have an equivalent accuracy of knowledge values, an equivalent number of decimal places because of the data values.

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### Exclusive Form – Definition

The exclusive form is defined as the series in which the upper limit is not included in the class and is included in an upcoming class. The exclusive series of a class type is a continuous series. Consider the example of the exclusive form is 0- 10, 10- 20, 20- 30, 30- 40, 40- 50 we can also see that the upper limit of the class is included in the next class interval. In exclusive form, the lower class limit and upper-class limit are known as true lower class limit and true upper-class limit of the interval.

### Inclusive Form of Class Limit – Definition

The inclusive form of class limit is defined as when the lower class limit and the upper-class limit are included, then it is an inclusive class interval. Consider the example of the inclusive form is 0- 10, 11- 20, 21- 20, 31- 40, etc are the inclusive type of class intervals. Usually, in the case of discrete variables, the inclusive form of class intervals is used.

The inclusive class limit series are obtained by subtracting 0.5 from the lower class limit and adding 0.5 to the upper-class limit. Therefore, class limits of 10- 20 class intervals in the inclusive form are 9.5 is the lower class limit and 20.5 is the upper-class limit.

### Related Terms to Class Limits

Below we have provided related terms of class limits along with their definitions in detail. They are explained as such

#### Class Mark

The classmark is also called the Class midpoint. The classmark is a specific point in the center of the categories in a frequency distribution table. Classmark is also the center of a bar in a histogram. It is defined as the average of the upper class and lower class limit.

Therefore, Class Mark = ½ (upper-class limit + lower class limit)

#### Class Size

The difference between the true lower class limit and the true upper-class limit is called Class size. The class size will always remain the same in all the class intervals.

#### Range

The difference between the maximum value of observation and the minimum value of observation is called Range.

### Difference between Exclusive and Inclusive Class Limits

Exclusive Class Limit | Inclusive Class Limit |
---|---|

1. When the upper limit of the class is excluded from the class and is included in the next class or upcoming class, it is called the exclusive class limit. | 1. In the inclusive class limit, the upper-class limit of a class interval is included in the class itself. |

2. Exclusive class limit is suitable for continuous variables. | 2. Inclusive class limit is suitable for discrete variables |

3. In the exclusive class limit, the class intervals are 10- 20, 20- 30, 30- 40. | 3. In the inclusive class limit, the class intervals are 10- 20, 21- 30, 31- 40. |

### Inclusive and Exclusive Class Interval Examples

**Problem 1: **

Find the upper-class limit in inclusive form for the class interval of 20- 25.

**Solution: **

Given, the class interval of 20- 25,

Now, we can find the upper-class limit of an inclusive

We know that in an inclusive class limit subtracting 0.5 on the lower class limit and adding 0.5 on the upper-class limit.

Here we find the upper-class limit. So, we can add 0.5 to the upper-class limit.

Therefore, the upper-class limit of an inclusive form is 25+ 0.5 = 25.5.

**Problem 2: **

Find the actual upper-class limit value, lower-class limit, and mid-value of the class interval 10- 15, 16- 20, 21- 25, 26- 30, 31- 35?

**Solution: **

Given the class interval 10- 15, 16- 20, 21- 25, 26- 30, 31- 35

Now we can find the values of upper-class limit, lower-class limit, and mid-value (or) class mark.

The Actual lower class limit value is 10.

The Actual upper-class limit value is 35.

Now, we can find the mid-value or class mark,

We know the formula of class mark i.e,

Class Mark = ½ (upper-class limit + lower class limit)

Substitute the upper-class value and lower class value in the above formula, we get

Class Mark = ½ (35 + 10) = ½ (45)

Class Mark = 22.5

Therefore, the mid value is 22.5

### FAQ’S on Class Limits in Exclusive and Inclusive Form

**1. What is a class limit?**

Class limit is defined as the minimum value and the maximum value of the class interval may be contained. The maximum value in the class is known as the Upper-class limit whereas the minimum value in the class is known as the Lower class limit.

**2. Define Range?**

The difference between the maximum value of observation and the minimum value of observation is called Range.

**3. Define Class Mark?**

The classmark is defined as the average of upper-class limit and lower class limit, the formula of classmark is,

Class Mark = ½ (upper-class limit + lower class limit)

**4. What are the full forms of LCL and UCL?**

LCL means Lower Class Limit and UCL means Upper-Class Limit.

**5. What is meant by the Inclusive Form of Class Limit?**

The inclusive form is defined as when the lower class limit and the upper-class limit are included, then it is an inclusive class interval. These are obtained by subtracting 0.5 from the lower class limit and adding 0.5 to the upper-class limit.