Statistics: Range Formula

The range is a simple yet useful measure of dispersion in statistics. It describes the total spread of a dataset by calculating the difference between the highest and lowest values. This guide provides a clear and concise overview of the range formula, empowering you to calculate and interpret the spread of data with ease.

Understanding the Range: The Span of Data

The range gives you an idea of how much the data varies. A larger range indicates greater variability, while a smaller range suggests the data points are clustered more closely together. While easy to calculate, the range is sensitive to outliers (extreme values).

Essential Range Formula:

The formula for calculating the range is straightforward:

• Range = Highest Value - Lowest Value

Illustrative Examples: Putting the Formula into Practice

Let's work through some examples to understand how to apply the range formula:

• Example 1: Find the range of the following dataset: 5, 2, 8, 1, 9.

  1. Identify the highest value: 9
  2. Identify the lowest value: 1
  3. Range = 9 - 1 = 8

• Example 2: Find the range of the following dataset: 12, 15, 10, 18, 14.

  1. Identify the highest value: 18
  2. Identify the lowest value: 10
  3. Range = 18 - 10 = 8

• Example 3: Find the range of the following dataset: -3, -1, 0, 2, 5.

  1. Identify the highest value: 5
  2. Identify the lowest value: -3
  3. Range = 5 - (-3) = 5 + 3 = 8

• Example 4: A set of measurements are recorded as: 2.5 cm, 3.1 cm, 2.8 cm, 3.5 cm, 2.2 cm. Find the range.

  1. Identify the highest value: 3.5 cm
  2. Identify the lowest value: 2.2 cm
  3. Range = 3.5 cm - 2.2 cm = 1.3 cm

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Applications of the Range:

The range is used in:

• Basic statistical analysis: It provides a quick measure of data spread.
• Quality control: Monitoring the range of measurements to ensure consistency.
• Descriptive statistics: Summarizing data variability.

Limitations of the Range:

It's important to remember that the range is highly sensitive to outliers. A single extreme value can significantly inflate the range, giving a misleading impression of the overall data spread. For this reason, it is often used in conjunction with other measures of dispersion like the interquartile range or standard deviation, which are less susceptible to outliers.

Conclusion: Understanding the Range

Understanding the range is a fundamental step in analyzing data variability. This guide provides a valuable resource for learning and applying this essential formula. By mastering this concept, you'll be better equipped to describe and interpret the spread of data in various contexts.

Call to Action:

Bookmark this page for quick reference and share it with others who might find it helpful. Practice applying the range formula to different datasets to reinforce your understanding. Remember to consider the potential influence of outliers when interpreting the range.