4.2:

4.2: Range

JoVE Core
Statistics

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JoVE Core Statistics

Range

4.1: What is Variation?

4.3: Standard Deviation

11,702 Views

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00:59 min

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April 30, 2023

Overview

The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:

15.9; 16.1; 15.2; 14.8; 15.8; 15.9; 16.0; 15.5

Measurements of the amount of soda in a 16-ounce can vary since different subjects record these measurements or since the exact amount – 16 ounces of liquid, was not poured into the containers. Manufacturers regularly perform tests to determine if the amount of soda in the can falls within the desired range. For the given dataset, the range is calculated as the difference between the largest and smallest values: 16.1 − 14.8 = 1.3.

The range relies heavily on the extreme values, that is, the maximum and minimum values. Hence, it is highly susceptible to outliers and lacks robustness in measurement. However, it is relatively easy to compute; therefore, it is used widely in statistical process control in manufacturing, as shown in the above example.

Transcript

The range is a measure of variation, defined as the difference between the maximum and minimum values.

Consider a dataset on the weights of different breeds of dogs. The difference between the weight of the heaviest breed of dog, the English Mastiff, and that of the smallest dog breed, the Chihuahua, gives the range of the dataset.

Here, the range value of 101 kg denotes the weight variation among different breeds of dogs. The average weight of any dog breed, in this example, will fall within this dispersion or spread.

The range relies only on the maximum and minimum, or extreme values, unlike other measures of variation. Therefore, the range has limited use because of its sensitivity to outliers and lack of robustness.

Since the range is easier to compute, it is often used to prepare control charts for manufacturing and weather forecasting applications.

Key Terms and definitions

Range (Main keyword) – The difference between the highest and lowest values of a dataset.
Outliers – A data point significantly different from others in a dataset.
Statistical Process Control – A method in statistical quality control in the manufacturing industry.
Can Range (related to keyword) – The different values recorded in manufactured items like soda cans.
Measurement Variation – Variation in measurements due to human recording or manufacturing errors.

Learning Objectives

Define Range – Explain what it is (e.g., the range in science).
Contrast Maximum vs Minimum – Describe the key differences (e.g., range stats).
Explore Examples – Describe practical scenario (e.g., example of range in statistics).
Explain susceptibility to outliers – Short description on the impact of outliers on the range.
Apply in Statistical Process Control– Discuss the application of range in quality control.

Questions that this video will help you answer

What is the range and how is it affected by outliers?
What is the difference between maximum and minimum values in a dataset?
How does the range provide insights in manufacturing industry?

This video is also useful for

Students – Helps to understand the concept of range and its role in statistics
Educators – Offers a clear understanding, aids in teaching the topic effectively.
Researchers – Imparts an understanding of measurement variations for conducting research.
Manufacturers - Provides techniques for quality control and process monitoring.

Tags

Range Variation Dataset Highest Value Lowest Value Measurement Outliers Statistical Process Control Manufacturing Soda Can Measurements Robustness Maximum Value Minimum Value