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# Class Interval|Definition & Meaning

## Definition

A class interval in a frequency distribution is used to denote the width of a class. This means that the classes formed in a grouped frequency distribution have a class interval defining its range and data taken in that range. Its usually calculated by subtracting the upper limit value from the lower limit value in a specific class to find its class interval.

## Organizing Data Using Classes and Class Intervals

Let us consider the **mark distribution** of a specific class of **10 students**. A set of marks of 10 students out of 25 are given: **23, 19, 12, 7, 3, 21, 17, 22, 11**, and **9**. From this data, we can construct a table as shown in the figure below:

From the figure, we can observe that we have five classes, each with a class interval of **four marks,** except for the **first class** having a class interval of **five marks.** Moreover, each class does not **overlap** with the other class. This is a typical example of an **inclusive class interval,** where the class’ limits do not overlap the **succeeding class.**

Moreover, this data can be used to create a **histogram,** which is used for a better analysis of the marks distribution of the class and identify **implicit information** from the data collected. This way, any data samplings can be organized and analyzed with the help of different classes and class intervals.

## Types of Class Intervals

There are two types of class intervals based on their **upper** and **lower limits** in each class: **Exclusive** **Class Interval,** and **Inclusive** **Class Interval.** These class intervals are differentiated by the upper and lower limits of one class to the succeeding class.

**Exclusive Class Intervals** are the type of class intervals where the **upper limit** of one class is **equal** to the **lower limit** of the succeeding class. Examples of such classes can be given: **10-20, 20-30, 30-40**, etc. In this case, the upper limit of a class is **excluded** from the range of the class and the lower limit is **included** in the class interval range.

The other type of class interval is the **Inclusive class interval**, Here, the class’s **upper limit** of the class is **different** from the **lower limit** of the succeeding class, hence **no overlapping** of values occurs. Thus, we usually **include both** the upper and lower bounds of the class in the range of the class.

Moreover, these different types of class intervals are used for different **applications.** Exclusive class intervals are used in applications that involve **continuous variables** and samples such as the length of a leaf in a tree. Inclusive class intervals are generally used in **compiling discrete variables,** such as compiling the marks distribution of a class.

## Significance of Class and Class Intervals

In **statistics** and **grouped frequency distribution**, the **data** is collected and arranged in a **class,** and the width of this class is known as the class interval. These classes help in organizing the data **systematically** and **ease** the process of **analysis** and **data research** in a given pool of **numerical** value. Furthermore, the class interval defines how wide the range of data is taken for organizing a set of values.

Using classes and their intervals, one can easily create a **histogram** to depict the data in a **graphical format** for understanding and analysis of the data by observing its trend and **frequency distribution** in given ranges and classes.

Classes provide a simple and organized **sampling** **of data** from a sample pool that is collected from **observation, experimentations,** or **surveys.** It is difficult to find an **implicit meaning** or analyze a given data pool that is **disorganized** and **randomized** with no systematic order to it. Thus, classes in a range of data provide the required order and organization to help in distinguishing the **underlying** information that is usually **missed out** while sampling data.

Additionally, the class intervals provided for a class can greatly **improve** the **accuracy** and **data organization** of a set of samples. In statistics, the right class interval can help greatly in the **orientation** of the data and analysis of given **disorganized** sample data.

Moreover, the data organized in classes can be used in many forms of depiction such as a histogram or a bar chart to further analyze the **implicit meanings** and trends that are given by the **sampled data.**

## An Example of Class Intervals and Their Applications

Below is a table provided with the measurements of the **length** of **thirty leaves** taken from the **same tree** in **July 2022.** Group the following data into **classes** and find the **approximate** **mean length** of leaves of **all thirty samples. **

### Solution

First of all, we create a grouped frequency table that has** 7 classes**: **20 – 29, 30 – 39, 40 – 49, 50 – 59, 60 – 69, 70 – 79,** and** 80 – 89.** The class interval of the given classes is 9. This is calculated by the following process:

**Class Interval = Upper bound limit – Lower bound Limit**

Class Interval = 49 – 40

Class Interval = **9**

Hence proven that the **class interval** of each class is **9**.

Afterward, we try to find the **average length** of the leaves across the thirty samples that were measured. For that, we first find the **midpoint** of all the classes. After finding the midpoint, we then further group the data into the **frequency** of **each class.** These frequency values and the midpoint are multiplied to find a **numerical value** for each class.

Moving on, we find the **sum** of all seven resulting values of the above calculation to find the **approximate sum of all leaves.** To find the **mean value,** we finally **divide** the resulting sum by **30 **to get the mean value.

Hence our** mean value** calculated is **52.5 mm.**

*All images/mathematical drawings were created with GeoGebra.*