Understanding how to find the range of a set of numbers is essential in various mathematical and statistical analyses. In this comprehensive step-by-step guide, we will explain the process of finding the range of a set. By following the outlined steps and grasping the underlying concepts, you will be able to determine the range accurately. Let's dive into the details.
Step 1: Gather the Numbers
Start by gathering the set of numbers for which you want to find the range. Ensure that you have all the values readily available.
Step 2: Arrange the Numbers
Arrange the numbers in ascending order from the lowest to the highest. This step allows you to easily identify the smallest and largest values in the set.
Step 3: Identify the Smallest and Largest Numbers
After arranging the numbers, locate the smallest value, which will be the first number in the ordered set. Similarly, identify the largest value, which will be the last number in the ordered set.
Step 4: Calculate the Range
To find the range, subtract the smallest number from the largest number. The result will be the difference between these two values.
Step 5: Interpret the Result
After performing the subtraction, the resulting value represents the range of the set. It indicates the extent of the spread or variation in the data.
Example:
Let's apply these steps to find the range of the following set of numbers: 10, 5, 8, 12, 3.
Step 1: Gather the Numbers:
10, 5, 8, 12, 3
Step 2: Arrange the Numbers:
3, 5, 8, 10, 12
Step 3: Identify the Smallest and Largest Numbers:
The smallest number is 3, and the largest number is 12.
Step 4: Calculate the Range:
12 - 3 = 9
Step 5: Interpret the Result:
The range of the set {10, 5, 8, 12, 3} is 9.
Conclusion:
Finding the range of a set involves arranging the numbers in ascending order, identifying the smallest and largest values, and calculating the difference between them. By following this step-by-step guide, you can accurately determine the range of any given set of numbers. Understanding the range provides valuable insights into the spread or variation within the data, aiding in statistical analysis and decision-making processes.