Solved Examples On Class Interval

Example 1: Create a frequency distribution using class intervals for the age of sample population

Here’s the data: 15, 18, 22, 28, 35, 42, 50, 52, 60, 65

Solution:

Let’s create a frequency distribution with class intervals:

Step 1: Creating Class Intervals:

To analyze this data effectively, let’s create class intervals to group the age. We’ll choose class intervals of width 10, starting from the lowest age.

Step 2: Determine the Range:

Range = Maximum Age – Minimum Age

Range = 65 – 15 = 50

Step 3: Choose the Number of Intervals:

Let’s choose 5 intervals for this example.

Step 4: Calculate the Interval Width:

The interval width is calculated by dividing the range by the number of intervals

Interval Width = Range / Number of Intervals

Interval Width = 50 / 5 = 10

Step 5: Set Up the Intervals

Now, we’ll create the class intervals based on the interval width:

• Class Interval 1: [15-25)
• Class Interval 2: [25-35)
• Class Interval 3: [35-45)
• Class Interval 4: [45-55)
• Class Interval 5: [55-65)

Now, the data has been organized into class intervals, and we have the frequency of data points within each interval.This distribution helps us see how many students fall into each age group, making it easier to analyze and summarize the data.

Example 2: Arrange the dataset of exam scores for a class of students in class interval

72, 85, 62, 91, 78, 54, 88, 96, 70, 68, 75, 82, 59, 93, 77, 64, 80, 87, 73, 89, 66, 71, 84, 92, 76, 61, 79, 86, 67, 90

Solution:

Steps involved in grouping score into class interval:

Step 1: Creating Class Intervals:

To analyze this data effectively, let’s create class intervals to group the scores. We’ll choose class intervals of width 10, starting from the lowest score.

Step 2: Determine the Range: The range of the data is the difference between the highest and lowest scores:

Range = Maximum Score – Minimum Score

Range = 96 – 54

Range = 42

Step 3: Choose the Number of Class Intervals: For this example, let’s use five class intervals to provide a reasonable level of detail:

• 50-59
• 60-69
• 70-79
• 80-89
• 90-99

Step 4: Calculate the Class Width: To determine the width of each class interval, divide the range by the number of intervals:

Class Width = Range / Number of Intervals

Class Width = 42 / 5

Class Width ≈ 8.4

Since class intervals should be meaningful whole numbers, let’s round up the class width to 9.

Step 5: Set the Boundaries: Now, set the lower and upper boundaries for each class interval:

• 50-59 (Lower Limit: 50, Upper Limit: 59)
• 60-69 (Lower Limit: 60, Upper Limit: 69)
• 70-79 (Lower Limit: 70, Upper Limit: 79)
• 80-89 (Lower Limit: 80, Upper Limit: 89)
• 90-99 (Lower Limit: 90, Upper Limit: 99)

Organize Data into Class Intervals: Group the exam scores into the appropriate class intervals based on the boundaries. For example, a score of 72 falls into the 70-79 class interval.

Example 3: Given the following data points, create class intervals with a width of 10

Data: 12, 18, 25, 30, 35, 42, 48, 55, 60, 65, 70

Solution:

1.Calculate the range:

Range = Maximum value – Minimum value

= 70 – 12 = 58.

2.Decide on the number of intervals (let’s say 5).

3.Calculate the interval width:

Width = Range / Number of intervals = 58 / 5 = 11.6 (round up to 12).

4.Set up the intervals:

1. [10, 22)
2. [22, 34)
3. [34, 46)
4. [46, 58)
5. [58, 70)

This creates five class intervals to represent the data effectively.

Class Interval in Statistics is an important element, particularly in organizing and summarizing data. It serves as a fundamental tool for grouping data points into meaningful categories, enabling a more manageable and insightful analysis. In this comprehensive article, we will delve into the concept of class intervals in statistics, their significance, and how to effectively create and utilize them.

Our exploration begins with a clear definition of class intervals and their role in statistical analysis. We will discuss the importance of choosing appropriate class intervals to reveal patterns, trends, and distributions within datasets. Whether you’re a student embarking on a statistics course or a data analyst seeking to enhance your data interpretation skills, this article is your guide to mastering class intervals.